Hyperbola: JEE Main Mathematics Previous Year Questions

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

1. $The equation of the hyperbola whose foci are (-2, 0) and (2, 0) and eccentricity is 2 is given by$
2. $The length of the chord of the parabola x^{2} = 4 y havingequation x - 2 y + 42 = 0 is:$
3. $The equation of the pair of asymptotes of the hyperbola x^{2} - 2 y^{2} - 8 x + 8 y + 4 = 0 is$
4. $Suppose that the circle x^{2} + y^{2} + 2 gx + 2 fy + c = 0 has its centre on 2 x + 3 y - 7 = 0 and cuts the circles x^{2} + y^{2} - 4 x - 6 y + 11 = 0 and\dots$
5. $The product of lengths of perpendicular from any point on the hyperbola x^{2} - y^{2} = 16 to its asymptotes, is$
6. $If x^{2} = 8 ay is the transformed equation of x^{2} - 4 y + 6 x + 15 = 0 when the origin is shifted to the point (α, β) by translat\dots$
7. $The point where the line 4 x - 3 y + 7 = 0 touches the circle x^{2} + y^{2} - 6 x + 4 y - 12 = 0 is$
8. $When the coordinate axes are rotated about the origin in the positive direction through an angle \frac{π}{4}, if the equation 49 x^{2} + 25 y^{2} = 1225 is transfo\dots$
9. $Let L be a normal to the parabola y2 = 4x. If L passes through the point (9, 6), then L is given by$
10. $The tangent to the curve xy = 25 at any point on it cuts the coordinate axes at A and B, then the area of the triangle OAB is$
11. $The centre of the circle passing through the points of intersection of the circles (x + 3)^{2} + (y + 2)^{2} = 25 and\dots$
12. $The radius of the circle whose center lies at (1, 2) while cutting the circle x^{2} + y^{2} + 4 x + 16 y - 30 = 0 orthogonally, is .......... units.$
13. $The values of m for which the line y = mx + 2 becomes a tangent to the hyperbola 4 x^{2} - 9 y^{2} = 36 is$
14. $x = 4 (1 + cos θ) and y = 3 (1 + sin θ) are the parametric equations of$
15. $If A and B are the points of intersection of the circle x^{2} + y^{2} - 8 x = 0 and the hyperbola \frac{x ^{2}}{9} - \frac{y ^{2}}{4} = 1 and a point P moves on th\dots$
16. $If e_{1} and e_{2} are the eccentricities of a hyperbola 3 x^{2} - 3 y^{2} = 25 and its conjugate, then$
17. $Area of a triangle formed by tangent and normal to the curve \frac{x ^{2}}{a ^{2}} + \frac{y ^{2}}{b ^{2}} = 1 at\dots$
18. $The equation of the circle whose radius is 3 and which touches internally the circle x^{2} + y^{2} - 4 x - 6 y - 12 = 0 at the point (- 1, - 1) is$
19. $If (a, b) is the centre of the circle passing through the vertices of the triangle formed by x + y = 6, 2 x + y = 4 and x + 2 y = 5, then\dots$
20. $The distance between the foci of a hyperbola is 16 and its eccentricity is 2 . Its equation is$
21. $The equation of the circle whose diameter is the common chord of the circles x^{2} + y^{2} + 2 x + 2 y + 1 = 0 and x^{2} + y^{2} + 4 x + 6 y + 4 = 0 is$
22. $Let e_{1} and e_{2} be the eccentricities of the ellipse \frac{x ^{2}}{b ^{2}} + \frac{y ^{2}}{25} = 1 and the hyperbola\dots$
23. $The value of a, such that the power of the point (1, 6) with respect to the circle x^{2} + y^{2} + 4 x - 6 y - a = 0, is -16 , is$
24. $A hyperbola, having the transverse axis of length 2 sin θ, is confocal with the ellipse 3 x^{2} + 4 y^{2} = 12. Then its equation is$
25. $A (- 2, 9) and B (1, 6) are two points on the curve y = x^{2} + 5 . The coordinates of the point C on the curve such that th\dots$

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Hyperbola: JEE Main Mathematics Previous Year Questions

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