JEE Main Mathematics — Ellipse Previous-Year Questions

Let the length of the latus rectum of an ellipse x²a²+y²b²=1,(a>b), be 30. If its eccentricity is the maximum value of…

Let (x²)/(f(a²+7a+3)) + (y²)/(f(3a+15)) = 1 represent an ellipse with major axis along y-axis, where f is a strictly de…

Let (h, k) lie on the circle C: x²+y²=4 and the point (2 h+1,3 k+2) lie on an ellipse with eccentricity e. Then the val…

Let S and Sⁱme be the foci of the ellipse x²25+y²9=1 and P(α, β) be a point on the ellipse in the first quadrant. If (S…

Let a focus of the ellipse E: (x²)/(a²) + (y²)/(b²) = 1 be S(4, 0) and its eccentricity be (4)/(5). If the point P(3, α…

Let an ellipse (x²)/(a²) + (y²)/(b²) = 1, a < b, pass through the point (4, 3) and have eccentricity √(5)3. Then the le…

Let x = 9 be a directrix of an ellipse E, whose centre is at the origin and eccentricity is (1)/(3). Let P(α, 0), α > 0…

Let A be the point (3, 0) and circles with variable diameter AB touch the circle x² + y² = 36 internally. Let the curve…

Let the line y-x=1 intersect the ellipse x²2+y²1=1 at the points A and B. Then the angle made by the line segment AB at…

Let each of the two ellipses E₁: x²a²+y²b²=1,(a>b) and E₂: x²~A²+y²~B²=1,(~A<B) have eccentricity (4)/(5). Let the leng…