Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
JEE Main202228 Jul 2022Evening ShiftMathematicsEllipseActual

Let the tangents at the points P and Q on the ellipse x 2 2 + y 2 4 = 1 meet at the point R 2 , 2 2 - 2 . If S is the focus of the ellipse on its negative major axis, then S P 2 + S Q 2 is equal to

Correct answer

0

Step-by-step solution

Given ellipse is x 2 2 + y 2 4 = 1   . . . . . . . . . . . 1 , So its eccentricity will be a 2 = b 2 1 - e 2 ⇒ 2 = 4 1 - e 2 ⇒ 1 2 = 1 - e 2 ⇒ e = 1 2 So, focus S will be S ≡ 0 , - a e ≡ 0 , - 2 Now, equation of chord of contact will be T = 0 ⇒ x 2 + 2 2 - 2 y 4 = 1 ⇒ x 2 = 1 - 2 - 1 y 2   . . . . . . . . . . 2 Now on solving equation 1   &   2 we get, ⇒ y = 0 , 2    &   x = 2 , 1 So points P   &   Q is given by

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