Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
JEE MainMathematicsEllipse

Let the length of the latus rectum of the ellipse x^2 36 + y^2 k ^2 = 1 , where 0 0 ) intersects the x -axis and y -axis at the points A and B , respectively. If the area of the circle having the line segment AB as a diameter is 25 , then the value of 2 + , where ( , ) is the centre of the circle, is equal to

Options

  1. A55
  2. B10
  3. C14
  4. D11

Correct answer

D. 11

Step-by-step solution

The equation of the ellipse is x^2 36 + y^2 k ^2 = 1 . Since 0 The length of the latus rectum is given by 2b^2 a = 3 . Substituting the values, we get 2 k ^2 6 = 3 k ^2 = 9 . Since k > 0 , we have k = 3 . The equation of the line L becomes 3x + 4y = . The points of intersection with the axes are A ( 3 , 0 ) and B (0, 4 ) . The length of the line segment AB is the diameter of the circle. Area of the circle = r^2 = 25 r = 5 . Thus, the diameter AB = 10 . Using the distance formula for AB : AB ^2 = ( 3 )^2 + ( 4 )^2 =

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