Description : Equation of tangent of the curve `y = 1 - e^(x//2)` at that point at which the curve crosses the y-axis, is :
Last Answer : Equation of tangent of the curve `y = 1 - e^(x//2)` at that point at which the curve crosses the y-axis, is ... `2x+y = 1` C. `x=-2y` D. None of these
Description : Find the equation of the tangent to the curve `x=theta+sin theta ,y=1+cos theta` at `theta=pi/4`
Last Answer : Find the equation of the tangent to the curve `x=theta+sin theta ,y=1+cos theta` at `theta=pi/4` A. ` ... 1+sqrt2)x+(sqrt2-1) pi` D. None of the above
Description : Find the equation of tangent of the curve `9x^(2)+16y^(2) = 144` at those points at which tangents are parallel to (i) X-axis, (ii) Y-axis.
Last Answer : Find the equation of tangent of the curve `9x^(2)+16y^(2) = 144` at those points at which tangents are parallel to (i) X-axis, (ii) Y-axis.
Description : Find the equation of tangent of the curve `y^(2) = 4x+5` which is parallel to the line ` 2x-y=5`.
Last Answer : Find the equation of tangent of the curve `y^(2) = 4x+5` which is parallel to the line ` 2x-y=5`.
Description : Find the point on the curve` y^(2) = x` at which the tangent drawn makes an angle of `45^(@)` from X-axis.
Last Answer : Find the point on the curve` y^(2) = x` at which the tangent drawn makes an angle of `45^(@)` from X-axis.
Description : Find the co-ordinates of that point on the curve `x^(2)/a^(2)+y^(2)/b^(2) = 1` at which the tangent drawn is parallel to Y-axis.
Last Answer : Find the co-ordinates of that point on the curve `x^(2)/a^(2)+y^(2)/b^(2) = 1` at which the tangent drawn is parallel to Y-axis.
Description : Find the co-ordinates of that point on the curve`y^(2)=x^(2)(1-x)` at which the tangent drawn is perpendicular to X-axis.
Last Answer : Find the co-ordinates of that point on the curve`y^(2)=x^(2)(1-x)` at which the tangent drawn is perpendicular to X-axis.
Description : Find the co-ordinates of that point on the curve `x^(3)+y^(3)= a^(3)` at which the tangent drawn is parallel to X-axis.
Last Answer : Find the co-ordinates of that point on the curve `x^(3)+y^(3)= a^(3)` at which the tangent drawn is parallel to X-axis.
Description : The tangent at any point P of a curve C meeta the x-axis at Q whose abscissa is positive and OP = OQ where O is origin, if C is a family of parabola h
Last Answer : The tangent at any point P of a curve C meeta the x-axis at Q whose abscissa is positive and OP = OQ ... , then find value of `(4(alpha+beta))/a` ?
Description : Find the inclination from X-axis of the tangent drawn of the following curves at the given points: (i) Curve`x^(2)-2y^(2)=8` at point (4, 2) (ii) Curv
Last Answer : Find the inclination from X-axis of the tangent drawn of the following curves at the given points: (i) Curve`x^(2)- ... `y^(2)=2x^(3)` at point (2, 4)
Description : What is the value of y when y equals 2x plus 1.25 is a tangent to the curve y squared equals 10x?
Last Answer : If the line y = 2x+1.25 is a tangent to the curve y^2 = 10x thenit works out that when x = 5/8 then y = 5/2
Description : Transition curves are introduced at either end of a circular curve, to obtain (A) Gradually decrease of curvature from zero at the tangent point to the specified quantity at the junction of the ... specified amount at the junction of the transition curve with main curve (D) None of these
Last Answer : (B) Gradual increase of super-elevation from zero at the tangent point to the specified amount at the junction of the transition curve with main curve
Description : If the radius of a main curve is 300 m and length of the transition curve is 100 m, the angle with tangent to locate the junction point, is (A) 1° 11' (B) 2° 11' (C) 3° 11' (D) 4° 11'
Last Answer : Answer: Option C
Description : What is the tangent line equation of the circle 2x2 plus 2y2 -8x -5y -1 equals 0 at the point 1 -1 on its circumference?
Last Answer : Circle equation: 2x^2 +2y^2 -8x -5y -1 = 0Divide all terms by 2: x^2 +y^2 -4x -2.5y -0.5 = 0Completing the squares: (x-2)^2 +(y-1.25)^2 = 6.0625Center of circle: (2, 1.25)Point of contact: (1 ... 9Tangent equation: y--1 = -4/9(x-1) => 9y = -4x -5Tangent line equation in its general form: 4x+9y+5 = 0
Description : What is the equation of the tangent line that meets the circle x2 -4x plus y2 -6y equals 4 at the point 6 4?
Last Answer : Circle equation: x^2 -4x +y^2 -6y = 4Completing the squares: (x-2)^2 +(y-3)^2 = 17Point of contact: (6, 4)Center of circle: (2, 3)Slope of radius: 1/4Slope of tangent line: -4Tangent equation: y-4 = -4(x-6) => y = -4x+28Tangent line equation in its general form: 4x+y-28 = 0
Description : Find the equation of normal to the curve `y(x-2)(x-3)-x+7=0` at that point at which the curve meets X-axis.
Last Answer : Find the equation of normal to the curve `y(x-2)(x-3)-x+7=0` at that point at which the curve meets X-axis.
Description : Find the equation of normals of the following curves at the given points: (i) Curve`y^(2)=4 ax" at point "(at^(2), 2at)`. (ii) Curve `y= e^(x)" at poi
Last Answer : Find the equation of normals of the following curves at the given points: (i) Curve`y^(2)=4 ax" at point "(at^( ... (2)-9y^(2) = 432` at point (6, 4).
Description : Find the equation of tangents of the following curves at the given points: (i) Curve`x^(2) = 25` at point (3, 4) (ii) Curve `y = 2x^(3) + 2x^(2) - 8x+
Last Answer : Find the equation of tangents of the following curves at the given points: (i) Curve`x^(2) = 25` at point (3, 4) ... 2)(x-1) = 4x^(2)` at point (5, 5)
Description : What is the point of contact when the tangent line y equals x plus c touches the circle x squared plus y squared equals 4?
Last Answer : The line meets the circle when:y = x + c→ x² + y² = 4→ x² + (x + c)² - 4 = 0→ x² + x² +2cx + c² - 4 = 0→ 2x² + 2cx + (c² - 4) = 0If the line is a tangent to the circle, this has a repeatedroot. This occurs ... 2 = 0→ (x + √2)² = 0→ x = -√2→ y = x + 2√2= -√2 + 2√2= √2→ point of contact is (-√2, √2)
Description : Pick up the correct statement from the following: (A) Long tangent sections exceeding 3 km in length should be avoided (B) Curve length should be at least 150 metres for a deflection angle of 5 ... decrease in the deflection angle, 30 metre length of curve to be increased (D) All the above
Last Answer : Answer: Option D
Description : In the bezier curve, the curve is always________to first and last segments of the polygon a.normal b.parallel c.tangent d.none of the above
Last Answer : c.tangent
Description : In the bezier curve, the curve is always to first and last segments of thepolygon a.normal b.parallel c.tangent d.none of the above
Description : For water-ethanol system, the minimum reflux ratio (A) Is computed from the slope of the upper operating line that is tangent to the equilibrium curve (B) Is computed from the intercept of the operating line (C) Cannot be computed (D) Is the optimum reflux ratio
Last Answer : (A) Is computed from the slope of the upper operating line that is tangent to the equilibrium curve
Description : If is the length of a sub-chord and is the radius of simple curve, the angle of deflection between its tangent and sub-chord, in minutes, is equal to (A) 573 S/R (B) 573 R/S (C) 1718.9 R/S (D) 1718.9 S/R
Last Answer : (D) 1718.9 S/R
Description : If the long chord and tangent length of a circular curve of radius R are equal the angle of deflection, is (A) 30° (B) 60° (C) 90° (D) 120°
Last Answer : D
Description : Perpendicular offset from a tangent to the junction of a transition curve and circular curve is equal to (A) Shift (B) Twice the shift (C) Thrice the shift (D) Four times the shift
Last Answer : (D) Four times the shift
Description : If D is the degree of the curve of radius R, the exact length of its specified chord, is (A) Radius of the curve sine of half the degree (B) Diameter of the curve sine of half the ... Diameter of the curve cosine of half the degree (D) Diameter of the curve tangent of half the degree
Last Answer : (B) Diameter of the curve × sine of half the degree
Description : The angle of intersection of a curve is the angle between (A) Back tangent and forward tangent (B) Prolongation of back tangent and forward tangent (C) Forward tangent and long chord (D) Back tangent and long chord
Last Answer : (A) Back tangent and forward tangent
Description : In a lemniscate curve the ratio of the angle between the tangent at the end of the polar ray and the straight, and the angle between the polar ray and the straight, is (A) 2 (B) 3 (C) 4/3 (D) 3/2
Last Answer : (D) 3/2
Description : The tangent length of a simple circular curve of radius R (A) R tan (B) R tan (C) R sin (D) R sin
Last Answer : Answer: Option B
Description : The total length of a valley formed by two gradients - 3% and + 2% curve between the two tangent points to provide a rate of change of centrifugal acceleration 0.6 m/sec2 , for a design speed 100 kmph, is (A) 16.0 m (B) 42.3 m (C) 84.6 m (D) None of these
Description : If the radii of a compound curve and a reverse curve are respectively the same, the length of common tangent (A) Of compound curve will be more (B) Of reverse curve will be more (C) Of both curves will be equal (D) None of these
Description : If `16l^2+9m^2=24lm+6l+8m+1` and the line `mx+ly=1` is tangent to circle `S_1=0` then the equation of circle `S_2=0` which touches `S_1=0` at `(0,0)`
Last Answer : If `16l^2+9m^2=24lm+6l+8m+1` and the line `mx+ly=1` is tangent to circle `S_1=0` then the equation of ... `3x^(2)+3y^(2)-8x-6y=0` D. none of theese
Description : Find the equation of normal of the curve `2y= 7x - 5x^(2)` at those points at which the curve intersects the line x = y.
Last Answer : Find the equation of normal of the curve `2y= 7x - 5x^(2)` at those points at which the curve intersects the line x = y.
Description : Find the equation of the normal to the curve `x = acostheta` and `y = b sintheta` at `theta`
Last Answer : Find the equation of the normal to the curve `x = acostheta` and `y = b sintheta` at `theta`
Description : Find the equation of the normal to the curve `y = 5x + x^2` which makes an angle `45^@` with x axis.
Last Answer : Find the equation of the normal to the curve `y = 5x + x^2` which makes an angle `45^@` with x axis.
Description : Prove that the curve `y^2=4x and x^2 +y^2 - 6x +1=0` touches each other at thepoint `(1, 2),` find the equation of the common tangents.
Last Answer : Prove that the curve `y^2=4x and x^2 +y^2 - 6x +1=0` touches each other at thepoint `(1, 2),` find the equation of the common tangents.
Description : The equation of a curve passing through `(2,7/2)` and having gradient `1-1/(x^2)` at `(x , y)` is (a) `( b ) (c) y=( d ) x^(( e )2( f ))( g )+x+1( h )
Last Answer : The equation of a curve passing through `(2,7/2)` and having gradient `1-1/(x^2)` at `(x , y)` is (a) `( b ) ... (2)+3` C. `xy=x+5` D. `xy=x^(2)+x+1`
Description : The standard equation of a cubic parabolic transition curve provided on roads, is (A) y = x3 /6 RL (B) y = x/6 RL (C) y = l²/6 RL (D) y = l3 /6 RL
Last Answer : Answer: Option A
Description : The standard equation of a cubical spiral transition curve provided on roads, is (A) y = l²/6RL (B) y = x3 /6RL (C) y = x2 /6RL (D) y = x/6RL
Description : Find the equations of tangent and normal to the ellipse `(x^2)/(a^2)+(y^2)/(b^2)=1` at `(x_1,y_1)`
Last Answer : Find the equations of tangent and normal to the ellipse `(x^2)/(a^2)+(y^2)/(b^2)=1` at `(x_1,y_1)`
Description : The slope of one of the common tangent to circle `x^(2)+y^(2)=1` and ellipse `x^(2)/4+2y^(2)=1` is `sqrt(a/b)` where `gcd(a, b)=1` then `(a+b)/2` is e
Last Answer : The slope of one of the common tangent to circle `x^(2)+y^(2)=1` and ellipse `x^(2)/4+2y^(2)=1` is ` ... `gcd(a, b)=1` then `(a+b)/2` is equal to
Description : What are the values of x y and k when the line y equals 3x plus 1 is a tangent to the circle x squared plus y squared equals k?
Last Answer : If y = 3x + 1 is a tangent to x² + y² = k (k > 0 since it isa square), then where they meet has a repeated root; they meetat:x² + (3x + 1)² = k→ x² + 9x² + 6x + 1 - k = 0→ 10x² + 6x + (1 - k) = 0This is the ... 3/10→ y = 3 -3/10 + 1 = 9/10 + 1 = 1/10→ point of contact is (-3/10, 1/10) with k = 1/10
Description : A satellite travels at a constant speed in a circular orbit. The acceleration of the satellite is w) zero x) toward the center of the orbit y) away from the center of the orbit z) at a tangent to the orbit
Last Answer : ANSWER: X -- TOWARD THE CENTER OF THE ORBIT
Description : For an object moving in uniform circular motion, the direction of the instantaneous acceleration vector is: w) tangent to the path of motion x) equal to zero y) directed radially outward z) directed radially inward
Last Answer : ANSWER: Z -- DIRECTED RADIALLY INWARD
Description : What is the distance from a point on the x axis to the centre of a circle when a tangent line at the point 3 4 meets the circle of x2 plus y2 -2x -6y plus 5 equals 0?
Last Answer : Circle equation: x^2 +y^2 -2x -6y +5 = 0Completing the squares: (x-1)^2 +(y-3)^2 = 5Centre of circle: (1, 3)Tangent line meets the x-axis at: (0, 5)Distance from (0, 5) to (1, 3) = 5 units using the distanceformula
Description : Find parametric equation for Y-coordinates of Hermite cubic spline curve having endpoints P0[4,4]; P1[8,5] a.2u3-3u2+2u+4 b.3u3-2u2-2u-4 c.2u3-3u2-2u-4 d.2u3+3u2+2u+4
Last Answer : a.2u3-3u2+2u+4
Description : An upgrade g1% is followed by a downgrade g2%. The equation of the parabolic curve of length L to be introduced, is given by (A) y = g [(g - g L] x² (B) y = [(g g L] x² (C) y = [(g - g L] x² (D) y = [(g g L] x²
Description : What is the solution when y equals 2x plus 1 is a tangent to the circle 5y2 plus 5x2 equals 1?
Last Answer : If y = 2x+1 is a tangent line to the circle 5y^2 +5x^2 = 1 thenthe point of contact is at (-2/5, 1/5) because it has equalroots
Description : What is the length of the tangent line from the point 8 2 to a point where it meets the circle x2 plus y2 -4x -8y -5 equals 0?
Last Answer : Equation of circle: x^2 +y^2 -4x -8y -5 = 0Completing the squares: (x-2)^2 +(y-4)^2 = 25 which is radiussquaredCenter of circle: (2, 4)Tangent line originates from: (8, ... angle triangleUsing Pythagoras theorem: distance^2 minus radius^2 = 15Therefore length of tangent line is the square root of 15