Parabola questions
264 published questions with worked solutions.
- If the tangent to the parabola y^2 = x at a point (α, β), (β > 0) is also a tangent to the ellipse, x^2 + 2y^2 = 1, then α is...
- Let A(4, −4) and B(9, 6) be points on the parabola, y^2 = 4x. Let C be chosen on the arc AOB of the parabola, where O is the...
- Axis of a parabola lies along x-axis. If its vertex and focus are at distances 2 and 4 respectively from the origin, on the...
- Equation of a common tangent to the circle x^2 + y^2 - 6x = 0 and the parabola, y^2 = 4x, is:
- The equation of a tangent to the parabola, x^2 = 8y, which makes an angle θ with the positive directions of x-axis, is:
- Let P(4, −4) and Q(9, 6) be two points on the parabola, y^2 = 4x and let X be any point on the arc POQ of this parabola, where O...
- Equation of a common tangent to the parabola y^2 = 4x and the hyperbola xy = 2 is:
- The length of the chord of the parabola x^2 = 4y having equation x - 2y + 4 2 = 0 is:
- If the parabolas y^2 = 4b(x - c) and y^2 = 8ax have a common normal, then which one of the following is a valid choice for the...
- The equation of common tangent to the curves y^2 = 16x and xy = −4, is:
- If one end of a focal chord AB of the parabola y^2=8x is at A ( 1 2 ,-2 ), then the equation of the tangent to it at B is -
- Let the latus rectum of the parabola y^2=4x be the common chord to the circles C_1 and C_2 each of them having radius 2 5 . Then,...
- Let the line L : 2x + y = pass through the point of the intersection P (in the first quadrant) of the circle x^2 + y^2 = 3 and...
- Let PQ be a chord of the parabola y² = 12x and the midpoint of PQ be at (4, 1). Then, which of the following point lies on the...
- Let the length of the focal chord PQ of the parabola y² = 12x be 15 units. If the distance of PQ from the origin is p, then 10p²...
- Suppose AB is a focal chord of the parabola y² = 12x of length l and slope m < √3. If the distance of the chord AB from the...
- Let a line perpendicular to the line 2x − y = 10 touch the parabola y² = 4(x − 9) at the point P. The distance of the point P...
- Let L₁, L₂ be the lines passing through the point P(0, 1) and touching the parabola 9x² + 12x + 18y − 14 = 0. Let Q and R be the...
- If y = mx + 4 is a tangent to both the parabolas, y^2=4x and x^2=2by, then b is equal to
- Let a line y = mx (m > 0) intersect the parabola, y^2=x at a point P, other than the origin. Let the tangent to it at P meet the...
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