Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
Highly selective Backlog Qs for JEE MainMathematicsEllipse

Let (x, y) be a variable point on the curve 4 x²+9 y²-8 x-36 y+15=0 . Then (x²-2 x+y²-4 y+5 )+ (x²-2 x+y²-4 y+5 ) is -

Options

  1. A325 36
  2. B36 325
  3. C13 25
  4. D25 13

Correct answer

A. 325 36

Step-by-step solution

array l 4 x²+9 y²-8 x-36 y+15=0 4 (x²-2 x )+9 (y²-4 y )=-15 4 (x²-2 x+1 )+9 (y²-4 y+4=-15+4+36 . 4(x-1)²+9(y-2)²=25 (x-1)² ( 5 2 )² + (y-2)² ( 5 3 )² =1 . .(1) x²-2 x+y²-4 y+5 (x-1)²+(y-2)² array of ((x-1)²+(y-2)² )= 25 9 of ((x-1)²+(y-2)² )= 25 4 = 25 9 + 25 4 = 325 36

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 Highly selective Backlog Qs for JEE Main PYQs