Ellipse: JEE Main Mathematics Previous Year Questions

146 previous year questions from Ellipse. Here are the 25 most important ones; open any question for the correct answer and a full step-by-step solution.

1. $The length of the latus rectum of an ellipse is 6 units and the distance between a focus and its nearest vertex on the major axis is \frac{5}{3} units. If e is the\dots$
2. $Let x = 4 be a directrix to an ellipse whose centre is at the origin and its eccentricity is \frac{1}{2} . If P (1, β), β > 0 is a poi\dots$
3. $The equation \frac{x ^{2}}{2 - λ} - \frac{y ^{2}}{λ - 5} - 1 = 0 represents an ellipse if$
4. $If the line x - 2 y = 12 is tangent to the ellipse \frac{x ^{2}}{a ^{2}} + \frac{y ^{2}}{b ^{2}} = 1 at the point (3, \frac{- 9}{2}) then the length o\dots$
5. $Let S and S^{’} be the foci of the ellipse \frac{x ^{2}}{25} + \frac{y ^{2}}{9} = 1 and P (α, β) be a point on the ellipse i\dots$
6. $Foci of the ellipse 2 x^{2} + 3 y^{2} - 4 x - 12 y + 13 = 0 are$
7. $If the line αx + 4 y = 7, where α \in R, touches the ellipse 3 x^{2} + 4 y^{2} = 1 at the point P in the first quadrant, then one of the focal di\dots$
8. $If the eccentricity and the length of the latus rectum of an ellipse \frac{x ^{2}}{a ^{2}} + \frac{y ^{2}}{b ^{2}} = 1 are \frac{3}{2} and 1 respectively, th\dots$
9. $The value of ' k' so that the line y = 2 x + k may touch the ellipse 3 x^{2} + 5 y^{2} = 15 is$
10. $The line x = 8 is the directrix of the ellipse E : \frac{x ^{2}}{a ^{2}} + \frac{y ^{2}}{b ^{2}} = 1 with the corresponding focus (2, 0) .\dots$
11. $If the normal to the ellipse 3 x^{2} + 4 y^{2} = 12 at a point P on it is parallel to the line, 2 x + y = 4 and the tangent to the ellipse at P passes through\dots$
12. $The sum of the squares of the eccentricities of the conics \frac{x ^{2}}{4} + \frac{y ^{2}}{3} = 1 and \frac{x ^{2}}{4} - \frac{y ^{2}}{3} = 1 is$
13. $If the latus rectum of an ellipse is equal to half of minor axis, then its eccentricity is$
14. $The radius of the circle passing through the foci of the ellipse \frac{x ^{2}}{16} + \frac{y ^{2}}{9} = 1 and having its centre at (0, 3) is$
15. $The angle between the tangents drawn from the point (1, 2) to the ellipse 3 x^{2} + 2 y^{2} = 5 is$
16. $Let S (1, 0) and S^{’} (0, 1) be the foci of an ellipse such that SP + S^{’} P = 2 for any point P o\dots$
17. $If the co-ordinate of two points A and B are (7, 0) and (- 7, 0) respectively and P is any point on the conic,\dots$
18. $The equation of the ellipse with directrix 3 x + 4 y - 5 = 0, focus (1, 2) and eccentricity \frac{1}{2}, is$
19. $If the tangent at a point P on the parabola y^{2} = 3 x is parallel to the line x + 2 y = 1 and the tangents at the points Q and R on the ellipse\dots$
20. $The foci of the ellipse \frac{x ^{2}}{16} + \frac{y ^{2}}{b ^{2}} = 1 and the hyperbola \frac{x ^{2}}{144} - \frac{y ^{2}}{81} = \frac{1}{25} coincide. Then, the value\dots$
21. $Let the length of the latus rectum of an ellipse with its major axis along x -axis and centre at the origin, be 8 . If the distance between the foci of this ellipse\dots$
22. $The eccentricity of the ellipse \frac{x ^{2}}{36} + \frac{y ^{2}}{16} = 1 is$
23. $P (θ_{1}) and Q (θ_{2}) are two points on the ellipse \frac{x ^{2}}{a ^{2}} + \frac{y ^{2}}{b ^{2}} = 1 with eccentricity\dots$
24. $Let the ellipse E : \frac{x ^{2}}{144} + \frac{y ^{2}}{169} = 1 and the hyperbola H : \frac{x ^{2}}{16} - \frac{y ^{2}}{λ ^{2}} = - 1 have the same foc\dots$
25. $The length of the latus-rectum of the ellipse, whose foci are (2, 5) and (2, - 3) and eccentricity is \frac{4}{5}, is$

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Ellipse: JEE Main Mathematics Previous Year Questions

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