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.

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.
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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.
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Last Answer : (a) Internal division: If P(x, y) divides the line segment formed by the joining of the points A (x1, y1) and B (x2, y2) internally in the ratio m1 : m2. Then\(x=rac{m_1x_2+m_2x_1}{m_1+m_2}\) and \(y=rac ... : 1, the co-ordinates of the mid-point are \(\bigg(rac{x_1+x_2}{2},rac{y_1+y_2}{2}\bigg)\).

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What are the co-ordinates of the foot of the perpendicular from the point (2, 3) on the line x + y – 11 = 0 ? -Maths 9th

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Last Answer : (d) 2x + 9y + 7 = 0PS being the median of ΔPQR, S is the mid-point of QR, i.e., Coordinates of S ≡ \(\bigg(rac{6+7}{2},rac{-1+3}{2}\bigg)\) = \(\bigg(rac{13}{2},1\bigg)\)Slope of line parallel to PS = Slope of PS= \(rac{1 ... y + 1) = \(rac{-2}{9}\)(x - 1), i.e., 9y + 9 = - 2x + 2 ⇒ 2x + 9y + 7 = 0.

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Find the equation of tangent of the curve ` x^(2)+y^(2)=5` at point (1, 2).

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Translate the polygon with co-ordinates A (3, 6), B (8, 11), & C (11, 3) by 2 units in X direction and 3 units in Y direction.

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What is the value of y when y equals 2x plus 1.25 is a tangent to the curve y squared equals 10x?

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What is the equation of the straight line passing through the point (4, 3) and making intercepts on the co-ordinates axes whose sum is –1 ? -Maths 9th

Description : What is the equation of the straight line passing through the point (4, 3) and making intercepts on the co-ordinates axes whose sum is –1 ? -Maths 9th

Last Answer : Diagonals of a rhombus bisect each other at right angles ⇒ Co-ordinates of mid-points of AC and BD are equal∴ 0 = \(\bigg(rac{4+(-2)}{2},rac{-5+(-1)}{2}\bigg)\) = (1, -3)Slope of BD = \(rac{-5+1}{4+2}\) = \(rac{-4}{6}\) ... (rac{3}{2}\) isy + 3 = \(rac{3}{2}\) (x - 1)⇒ 2y + 6 = 3x - 3 ⇒ 2y = 3x - 9.

For a ternary mixture, in which equilateral triangular co-ordinate is used in leaching and extraction, a __________ of the equilateral triangular co-ordinates. (A) Binary mixture is represented by the apex (B) Binary mixture is represented by any point inside (C) Ternary mixture is represented by the sides (D) Pure component is represented by the apex

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Let R be the rectangular window against which the lines are to be clipped using 2D Sutherland-Cohen line clipping algorithm. The rectangular window has lower left-hand corner at (-5,1) and upper righthand corner at (3,7). Consider the following three lines for clipping with the given end point co-ordinates: Line AB: A(-6,2) and B(-1,8) Line CD: C(-1,5) and D(4,8) Line EF: E(-2,3) and F(1,2) Which of the following line(s) is/are candidate for clipping? (A) AB (B) CD (C) EF (D) AB and CD

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Dew point of an air-water vapor mixture (A) Decreases with decrease in pressure (B) At constant humidity & total pressure is fixed (C) Corresponding to any point on the humidity chart is obtained by projecting a line through this point parallel to the temperature axis and to the saturation curve (D) All 'a', 'b' & 'c'

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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.

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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 transition curve with main curve (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 (C) Gradual change of gradient from zero at the tangent point to the specified amount at the junction of the transition curve with main curve (D) None of these

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The line x – 4y = 6 is the perpendicular bisector of the segment AB and the co-ordinates of B are (1, 3). Find the co-ordinates of A. -Maths 9th

Description : The line x – 4y = 6 is the perpendicular bisector of the segment AB and the co-ordinates of B are (1, 3). Find the co-ordinates of A. -Maths 9th

Last Answer : Co-ordinates of A are \(\bigg(rac{3 imes9+1 imes5}{3+1},rac{3 imes6+1 imes-2}{3+1}\bigg)\) = \(\bigg(rac{32}{4},rac{16}{4}\bigg)\), i.e. (8, 4)Now, \(x\) - 3y + 4 = 0 ⇒ -3y = -\(x\) - 4 ⇒ y = \(rac{x}{3}+rac{4} ... 8) [Using, y - y1 = m (x - x1)]⇒ 3y - 12 = \(x\) - 8 ⇒ 3y - \(x\) = 4.

A supply curve parallel to X axis means the product supply is (a) Limited ; (b) Unlimited ; (c) Not available ; (d) None

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An incident ray comes in parallel to the principle axis of a concave mirror. Is it reflected: w) back along the incident ray x) at 30 degrees to incident ray y) through the focal point z) through the center of curvature

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Supply curve passing through any point on Y axis(Price) will have elasticity (a) Less than 1 ; (b) More than 1 ; (c) Just One ; (d) Zero

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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?

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)

Any convenient co-ordinate system or Cartesian co-ordinates which can be usedto define the picture is called a.spherical co-ordinates b.vector co-ordinates c.viewport co-ordinates d.world co-ordinates

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Last Answer : d.world co-ordinates

Co-ordinates are ranging according to the screen resolution. a.TRUE b.FALSE c. d.

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Which co-ordinates allow common vector operations such as translation, rotation,scaling and perspective projection to be represented as a matrix by which the vector is multiplied? a.vector co-ordinates b.3D co-ordinates c.affine co-ordinates d.homogenous co-ordinates

Description : Which co-ordinates allow common vector operations such as translation, rotation,scaling and perspective projection to be represented as a matrix by which the vector is multiplied? a.vector co-ordinates b.3D co-ordinates c.affine co-ordinates d.homogenous co-ordinates

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Draw the graph of the equation 3x + 4y = 12 and find the co-ordinates of the points of intersection of the equation with the co-ordinate axes. -Maths 9th

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Last Answer : Solution :-

What do you mean by Co-ordinates (Abscissa and Ordinate)? Explain with figure. -Maths 9th

Description : What do you mean by Co-ordinates (Abscissa and Ordinate)? Explain with figure. -Maths 9th

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Distance Formula for co-ordinates: -Maths 9th

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Section formula for co-ordinates: -Maths 9th

Description : Section formula for co-ordinates: -Maths 9th

Last Answer : The co-ordinate axes separate the plane into four regions called the quadrants. By custom the quadrants are numbered I, II, III, IV, in the counter clockwise direction as shown in the figure. (i) For distances along the x- ... +)X′OY′3rd quadrantx < 0, y < 0(-, -)XOY′4th quadrantx > 0, y < 0(+, -)

Find the co-ordinates of the circumcentre of the triangle whose vertices are (3, 0), (–1, –6) and (4, –1). Also find its circum-radius. -Maths 9th

Description : Find the co-ordinates of the circumcentre of the triangle whose vertices are (3, 0), (–1, –6) and (4, –1). Also find its circum-radius. -Maths 9th

Last Answer : Let A ≡ (2, - 2), B ≡ (-2, 1), C ≡ (5, 2 ). Then,AB = \(\sqrt{(-2-2)^2+(1+2)^2}\) = \(\sqrt{16+9}\) = \(\sqrt{25}\) = 5BC = \(\sqrt{(5+2)^2+(2-1)^2}\) = \(\sqrt{49+1}\) = \(\sqrt{50}\) = \( ... of ΔABC = \(rac{1}{2}\) x base x height = \(rac{1}{2}\) x AB x AC = \(rac{1}{2}\)x 5 x 5 = 12.5 sq. units.

Let the opposite angular points of a square be (3, 4) and (1, – 1), Find the co-ordinates of the remaining angular points. -Maths 9th

Description : Let the opposite angular points of a square be (3, 4) and (1, – 1), Find the co-ordinates of the remaining angular points. -Maths 9th

Last Answer : P ≡ (-3, 2), Q ≡ (-5, -5), R ≡ (2, -3), S ≡ (4, 4)∴ PQ = \(\sqrt{(-5+3)^2+(-5-2)^2}\) = \(\sqrt{4+49}\) = \(\sqrt{53}\)QR = \(\sqrt{(2+5)^2+(-3+5)^2}\) = \(\sqrt{49+4}\) = \ ... of rhombus = \(rac{1}{2}\) x (Product of length of diagonals) = \(rac{1}{2}\) x \(5\sqrt2\) x \(9\sqrt2\) = 45 sq. units.

The co-ordinates of mid-points of sides of a triangle are (1, 2), (0, –1) and (2, –1). Find its centroid. -Maths 9th

Description : The co-ordinates of mid-points of sides of a triangle are (1, 2), (0, –1) and (2, –1). Find its centroid. -Maths 9th

Last Answer : ABCD is a parallelogram, if the mid-points of diagonals AC and BD have the same co-ordinates (∵ Diagonals of a parallelogram bisect each other)Co-ordinates of mid-point of AC are \(\bigg(rac{a+2}{2},rac{-11+15}{2}\bigg)\) = \(\bigg(rac ... \(rac{a+2}{2}\) = 3 and 2 = \(rac{b+1}{2}\) ⇒ a = 4, b = 3.

In the adjoining figure, P and Q have co-ordinates (4, 6)and (0, 3) respectively. Find (i) the co-ordinates of R (ii) Area of quadrilateral OAPQ. -Maths 9th

Description : In the adjoining figure, P and Q have co-ordinates (4, 6)and (0, 3) respectively. Find (i) the co-ordinates of R (ii) Area of quadrilateral OAPQ. -Maths 9th

Last Answer : Let the line 2x + 3y - 30 = 0 divide the join of A(3, 4) and B(7, 8) at point C(p, q) in the ratio k : 1. Then,p = \(rac{7k+3}{k+1}\), q = \(rac{8k+4}{k+1}\)As the point C lies on the line 2x + 3y - 30 ... {3}{2}+1},rac{8 imesrac{3}{2}+4}{rac{3}{2}+1}\bigg)\) = \(\big(rac{27}{5},rac{32}{5}\big)\).