Parabola: JEE Main Mathematics Previous Year Questions

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

1. $The equation of directrix of parabola x^{2} + 8 x + 12 y + 4 = 0 is$
2. $For any real number t, the point (\frac{8 t}{1 + t ^{2}}, \frac{4 ( 1 - t ^{2} )}{1 + t ^{2}}) lies on a / an on a/an$
3. $If y = mx + 4 is a tangent to both the parabola y^{2} = 4 x and x^{2} = 2 by . Then the value of b is :$
4. $Let one end of a focal chord of the parabola y^{2} = 16 x be (16,16). If P (α, β) divides this focal chord internally in the ratio\dots$
5. $Two cards are drawn successively with replacement from a well-shuffled deck of 52 cards. Let X denote the random variable of number of aces obtained in the two draw\dots$
6. $If one end of diameter of the circle x^{2} + y^{2} - 4 x - 6 y + 11 = 0 is (3, 4), then the other end of the diameter is$
7. $The Cartesian form of the curve given by x = \frac{a}{2} (t + \frac{1}{t}), y = \frac{a}{2} (t - \frac{1}{t}), t is a parameter, is$
8. $For the parabola y^{2} = 4 x, the point P whose focal distance is 17 , is$
9. $The focus of the parabola y^{2} = 4 x + 16 is the centre of the circle C of radius 5 . If the values of λ, for which C passes through the point of intersecti\dots$
10. $The locus of a point on the argand plane represented by the complex number z, when z satisfies the condition\dots$
11. $The line x + 2 y = k meets the curve 2 x^{2} - 2 xy + 3 y^{2} + 2 x - y - 1 = 0 at two points A and B . Let O be the origin. If the line segments OA and\dots$
12. $Let the curve C be the mirror image of the parabola y2 = 4x with respect to the line x + y + 4 = 0. If A and B are the points of intersection of C with the line y= - 5, t\dots$
13. $The values that m can take, so that the straight line y = 4 x + m touches the curve x^{2} + 4 y^{2} = 4 is$
14. $If x^{2} + y^{2} + 6 x + 2 ky + 25 = 0 to touch Y -axis, then k =$
15. $If the x - intercept of a focal chord of the parabola y^{2} = 8 x + 4 y + 4 is 3, then the length of this chord is equal to ______$
16. $The urns A, B and C contain 4 red, 6 black; 4 red, 5 black and λ red, 5 black balls respectively. One of the urns is selected at random and a ball is drawn. If\dots$
17. $Let the parabola y = x^{2} + p x - 3, meet the coordinate axes at the points P, Q and R . If the circle C with centre at (- 1, - 1) passes thr\dots$
18. $If the circles x^{2} + y^{2} - 2 x - 2 y + k = 0 and x^{2} + y^{2} + 4 x + 6 y + 4 = 0 touch each other externally, then the point of contact of the two circles is$
19. $If the chord joining the points P_{1} (x_{1}, y_{1}) and P_{2} (x_{2}, y_{2}) on the parabola y^{2} = 12 x subtends a\dots$
20. $Two parabolas have the same focus (4, 3) and their directrices are the x -axis and the y -axis, respectively. If these parabolas intersects at\dots$
21. $Let O be the vertex of the parabola x^{2} = 4 y and Q be any point on it. Let the locus of the point P, which divides the line segment OQ internally in the ratio\dots$
22. $The angle between y^{2} = 4 x and x^{2} + y^{2} = 12 at a point of their intersection is$
23. $The sum of the reciprocals of focal distances of a focal chord PQ of y^{2} = 4 ax is$
24. $Let P be any point on the circle x^{2} + y^{2} - 2 x - 1 = 0 and C be its centre. Let AB be the chord of contact of P with respect to the circle\dots$
25. $If the point P on the curve, 4 x^{2} + 5 y^{2} = 20 is farthest from the point Q (0, - 4), then P Q^{2} is equal to:$

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Parabola: JEE Main Mathematics Previous Year Questions

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