Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
Most Important Selected Qs for JEE AdvancedMathematicsEllipse

A straight line through a point P( , 2),( 0) meets the ellipse x^2 9 + y^2 4 =1 at A and D & meets axes at B and C such that PA, PB, PC and PD are in GP, then ' ' can lie in interval

Options

  1. A[7, )
  2. B(-12,-8)
  3. C(-5,0)
  4. D(10, )

Correct answer

D. (10, )

Step-by-step solution

Any point on the line through P( , 2) is ( +r , 2+r ) and meets the ellipse x^2 9 + y^2 4 =1 at A and D ( +r )^2 9 + (2+r )^2 4 =1 (4 ^2 +9 ^2 ) r^2+4(2 +9 ) r+4 ^2=0 P A P D= 4 ^2 4 ^2 +9 ^2 Again solving with x y=0 PB PC = 2 4 ^2 4 ^2 +9 ^2 = 2 aligned & 2 2 +5 2 =13 & -1 13 4 ^2+25 1 | | 6 aligned

Practice Ellipse on Quantrex Academy →

More from Ellipse

Consider the ellipse E given by x^2 18 + y^2 12 = 1 . Let H be the hyperbola whose eccentricity is the reciprocal of the eccentricity of E and whose foci are the same as that of E 2026Passage: Consider the ellipses given by x^2 + 4y^2 = 1 and 4x^2 + y^2 = 1 . Question: Let P be the point in the first quadrant where the given ellipses intersect. If is the acute a 2026Let x^2 f(a^2+7a+3) + y^2 f(3a+15) = 1 represent an ellipse with major axis along y -axis, where f is a strictly decreasing positive function on R . If the set of all possible valu 2026The eccentricity of an ellipse E with centre at the origin O is 3 2 and its directrices are x = 4 6 3 . Let H: x^2 a^2 - y^2 b^2 = 1 be a hyperbola whose eccentricity is equal to t 2026Let x = 9 be a directrix of an ellipse E , whose centre is at the origin and eccentricity is 1 3 . Let P( , 0) , > 0 , be a focus of E and AB be a chord passing through P . Then th 2026Let a focus of the ellipse E: x^2 a^2 + y^2 b^2 = 1 be S(4, 0) and its eccentricity be 4 5 . If the point P(3, ) lies on E and O is the origin, then the area of POS is equal to: 2026Let A be the point (3, 0) and circles with variable diameter AB touch the circle x^2 + y^2 = 36 internally. Let the curve C be the locus of the point B. If the eccentricity of C is 2026Let an ellipse x^2 a^2 + y^2 b^2 = 1 , a < b , pass through the point (4, 3) and have eccentricity 5 3 . Then the length of its latus rectum is : 2026 Full Ellipse list All Most Important Selected Qs for JEE Advanced PYQs