Description : A parabola is drawn through two given points `A(1,0)` and `B(-1,0)` such that its directrix always touches the circle `x² + y^2 = 4.` Then, The locus
Last Answer : A parabola is drawn through two given points `A(1,0)` and `B(-1,0)` such that its directrix always touches the circle ... `(x^(2))/(5)+(y^(2))/(4)=1`
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 : If `x=9` is the chord of contact of the hyperbola `x^2-y^2=9` then the equation of the corresponding pair of tangents is (A) `9x^2-8y^2+18x-9=0` (B) `
Last Answer : If `x=9` is the chord of contact of the hyperbola `x^2-y^2=9` then the equation of the corresponding pair of ... 0` D. `9x^(2)-8y^(2) +18x+9=0`
Description : For setting out a simple curve, using two theodolites. (A) Offsets from tangents are required (B) Offsets from chord produced are required (C) Offsets from long chord are required (D) None of these
Last Answer : (D) None of these
Last Answer : (C) R/20
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 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 : Find the coordinates of the points on the curve `y=x^2+3x+4,` the tangents at which pass through the origin.
Last Answer : Find the coordinates of the points on the curve `y=x^2+3x+4,` the tangents at which pass through the origin.
Description : In a purely cohesive soil, the critical centre lies at the intersection of (A) Perpendicular bisector of slope and the locus of the centre (B) Perpendicular drawn at 1/3rd slope from toe and the ... C) Perpendicular drawn at 2/3rd slope from toe and the locus of the centre (D) Directional angles
Last Answer : Answer: Option D
Description : 26. The points of contact of the tangents drawn from the origin to the curve y=sinx, lie on the curve
Last Answer : 26. The points of contact of the tangents drawn from the origin to the curve y=sinx, lie on the curve A. `x^(2) ... x^(2)=x^(2)y^(2)` D. None of these
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 : 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 : Prove that the length of the tangents drawn from an external point to a circle are equal, hence show that the centre lies on the bisector of the angle between the two tangents? -SST 10th
Last Answer : Given: PT and TQ are two tangent drawn from an external point T to the circle C (O, r). To prove: 1. PT = TQ 2. ∠OTP = ∠OTQ Construction: Join OT. Proof: We know that, a tangent to ... point to a circle are equal. ∠OTP = ∠OTQ, ∴ Centre lies on the bisector of the angle between the two tangents.
Description : Draw a circle of diameter 6.4 cm. Then draw two tangents to the circle from a point P at a distance 6.4 cm from the centre of the circle. -Maths 9th
Last Answer : clear .
Description : How many tangents can be drawn at any point of a circle ?
Last Answer : A tangent can be drawn at any point in a circle.
Description : The locus of the middle points of the focal chords of the parabola, `y^2=4x` is:
Last Answer : The locus of the middle points of the focal chords of the parabola, `y^2=4x` is: A. `y^2=x-1` B. `y^2=2(x-1)` C. `y^2=2(1-x)` D. None
Description : What are the points of intersection of the line 2x plus 5y equals 4 with the curve y squared equals x plus 4?
Last Answer : If: 2x +5y = 4 then 25y^2 = 4x^2 -16x +16If: y^2 = x +4 then 25y^2 = 25x +100So: 4x^2 -16x +16 = 25x +100Transposing terms: 4x^2 -41x -84 = 0Factorizing the above: (4x+7)(x-12) = 0 meaning x = -7/4 or x =12By substitution into original equation points of intersection:(-7/4, 3/2) and (12, -4)
Description : Human Extremeties Temp Well Below Ambient?
Last Answer : Poor circulation frequently can cause such a feeling. You might want to mention this to your doctor so they can check your circulation. I find taking a Vitamin E capsule every morning helps my circulation. Welcome to Fluther!!!
Description : The locus of a point on a thread unwound from a cylinder will be a.A circle b.A cycloid c.A straight line d.A spiral e.An involute
Last Answer : b. A cycloid
Description : A point moves in such a manner that its distance from a fixed point is equal to its distance from a fixed line multiplied by a constant greater than one. The locus of the path traced by the point will be a a.Cycloid b.Hyperbola c.Circle d.Involute e.Ellipsc
Last Answer : d. Involute
Description : The locus of reaction of a two hinged semi-circular arch, is (A) Straight line (B) Parabola (C) Circle (D) Hyperbola
Last Answer : (A) Straight line
Description : The locus of the moment of inertia about inclined axes to the principal axis, is (A) Straight line (B) Parabola (C) Circle (D) Ellipse
Last Answer : (D) Ellipse
Description : The locus of the end point of the resultant of the normal and tangential components of the stress on an inclined plane, is (A) Circle (B) Parabola (C) Ellipse (D) Straight line
Last Answer : (C) Ellipse
Description : Which of the following is the locus of a point that moves in such a manner that its distance from a fixed point is equal to its distance from a fixed line multiplied by a constant greater than one (A) Ellipse (B) Hyperbola (C) Parabola (D) Circle
Last Answer : (B) Hyperbola
Description : What are the points of intersection between the line 3x -y equals 5 and the curve 2x squared plus y squared equals 129?
Last Answer : If: 3x-y = 5 then y^2 = (3x_5)^2 => 9x^2 -30x+25If: 2x^2 + y^2 = 129 then y^2 = 129-2x^2So: 9x^2 -30x+25 = 129-2x^2Transposing terms: 11x^2 -30x -104 = 0Factorizing the above: (11x- ... x = 52/11 or x= -2By substituting x into the original equation intersections areat: (52/11, 101/11) and (-2, -11)
Description : Find the equation of the circle which touches the both axes in first quadrant and whose radius is a. -Maths 9th
Last Answer : circle of radius a touches both axis in 1st quadrant so its centre will be (a,a). ∴ Required equation ⇒(x−a)2+(y−a)2=a2 ⇒x2+a2−2ax+y2+a2−2ay=a2 ⇒x2+y2−2ax−2ay+2a2−a2=0 ⇒x2−y2−2ax−2ay+a2=0.
Last Answer : Given that the circle of radius ‘a’ touches both axis. So, its centre is (a, a) So, the equation of required circles is : (x-a)2 + (y-a)2 = a2 ⇒ x2 - 2ax + a2+y2 - 2ay + a2 = a2 ⇒ x2 + y2 - 2ax - 2ay + a2 = 0
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 : What is the length of a tangent line from the point 7 -2 to a point when it touches the circle x2 plus y2 -10 equals 49?
Last Answer : x² + y² - 10 = 49→ x² + y² = 59= (x - 0)² + (y - 0)² = (√59)²→ circle has centre (0, 0) - the origin - and radius √59The point (7, -2) has a distance from the centre of the circleof:√((7 - 0)² + (-2 - 0)²) = √(7² + (-2)²) = √(49 + 4) = √53
Description : What is the straight line which touches the circumference in a circle?
Last Answer : It is the tangent of the circle
Description : Pick up the correct statement from the following: (A) The surface defined by the locus of points having same phase, is called a wave front (B) The wave whose surface of constant phase are parallel planes, ... waves is important and not the absolute phase of a point on the wave (D) All of these
Description : A chord of a circle of radius 7.5 cm with centre 0 is of length 9 cm. Find its distance from the centre. -Maths 9th
Last Answer : ∵ PM = MQ = 1/2 = PQ = 45 cm and OP = 7.5 cm In right angled ΔOMP, using phthagoras theorem OM2 = OP2 - PM2 ⇒OM2 = 7.52 - 4.52 ⇒OM2 = 56.25 - 20.25 ⇒OM2 = 36 ∴ OM = √36 = 6 cm
Description : A circle with centre O and diameter COB is given. If AB and CD are parallel, then show that chord AC is equal to chord BD. -Maths 9th
Last Answer : O Join AC and BD. Given, COB is the diameter of circle. ∠CAB = ∠BDC = 90° [angle in a semi-circle] Also, AB II CD ∠ABC = ∠DCB (alternate angles] Now, ∠ACB = 90° - ∠ABC and ∠DBC = 90° - ∠DCB = ... = ∠DBC BC = BC [common sides] ΔABC = ΔDCB [by ASA congruency] ∴ AC = BD [by CPCT] Hence Proved.
Description : The given figure shows a circle with centre O in which a diameter AB bisects the chord PQ at the point R. If PR = RQ = 8 cm and RB = 4 cm, then find the radius of the circle. -Maths 9th
Last Answer : Let r be the radius, then OQ = OB = r and OR = (r - 4) ∴ OQ2 = OR2 + RO2 ⇒ r2 = 64 + (r-4)2 ⇒ r2 = 64 + r2 + 16 - 8r ⇒ 8r = 80 ⇒ r = 10 cm
Description : AD is a diameter of a circle and AB is a chord. If AD = 34 cm, AB = 30 cm, then find the distance of AB from the centre of the circle. -Maths 9th
Last Answer : ∵ The perpendicular drawn from the centre to the chord bisects it. ∴ AM = 1/2 AB = 1/2 × 30 cm = 15 cm Also, OA = 1/2 AD = 1/2 × 34 cm = 17 cm In rt. △OAM, we have OA2 = OM2 + AM2 172 = OM2 + 152 ⇒ 289 = OM2 + 225 ⇒ OM2 = 289 - 225 ⇒ OM2 = 64 ⇒ OM = √64 = 8 cm
Description : In the figure, chord AB of circle with centre O, is produced to C such that BC = OB. CO is joined and produced to meet the circle in D. -Maths 9th
Last Answer : In △OBC, OB = BC ⇒ ∠BOC = ∠BCO = y ...[angles opp. to equal sides are equal] ∠OBA is the exterior angle of △BOC So, ∠ABO = 2y ...[ext. angle is equal to the sum of int. opp. angles] Similarly, ∠AOD is the exterior angle of △AOC ∴ x = 2y + y = 3y
Description : AD is a diameter of a circle and AB is a chord. If AD = 34 cm, AB = 30 cm, the distance of AB from the centre of the circle is -Maths 9th
Last Answer : (d) Given, AD = 34 cm and AB = 30 cm In figure, draw OL ⊥ AB. Since, the perpendicular from the centre of a circle to a chord bisects the chord.
Description : If the perpendicular bisector of a chord AB of a circle PXAQBY intersects the circle at P and Q, prove that arc PXA = arc PYB. -Maths 9th
Last Answer : Let AB be a chord of a circle having centre at OPQ be the perpendicular bisector of the chord AB, which intersects at M and it always passes through O. To prove arc PXA ≅ arc PYB Construction Join AP and BP. Proof In ... ΔBPM, AM = MB ∠PMA = ∠PMB PM = PM ∴ ΔAPM s ΔBPM ∴PA = PB ⇒arc PXA ≅ arc PYB
Description : A chord of a circle is equal to its radius. Find the angle subtended by this chord at a point in major segment. -Maths 9th
Last Answer : Given, AB is a chord of a circle, which is equal to the radius of the circle, i.e., AB = BO …(i) Join OA, AC and BC. Since, OA = OB= Radius of circle OA = AS = BO
Description : If two equal chords of a circle intersect, prove that the parts of one chord are separately equal to the parts of the other chord. -Maths 9th
Last Answer : Explanation of this question
Description : What is the relationship between chord of a circle and a perpendicular to it from the centre? -Maths 9th
Last Answer : Solution :- Perpendicular line from the centre bisect the chord.