Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
JEE Main202225 Jun 2022Evening ShiftMathematicsEllipseActual

The line y = x + 1 meets the ellipse x 2 4 + y 2 2 = 1 at two points P and Q . If r is the radius of the circle with P Q as diameter then 3 r 2 is equal to

Options

  1. A20
  2. B12
  3. C11
  4. D8

Correct answer

A. 20

Step-by-step solution

Plotting the diagram of given data we have, Let P be the point - 1 + p 2 , p 2 Since it lies on the ellipse x 2 4 + y 2 2 = 1 , we get - 1 + p 2 2 4 + p 2 2 2 = 1   ⇒ 3 p 2 8 - p 2 2 - 3 4 = 0 Here p 1 - p 2 2 = 2 2 3 2 - 4 - 2 = 8 9 + 8 = 80 9 We know, p 1 - p 2 2 = P Q 2 ⇒   P Q 2 = 80 9 Now r = P Q 2 ⇒ 9 r 2 = 9 P Q 2 4 = 9 4 × 80 9 = 20

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 JEE Main PYQs