Parabola questions
264 published questions with worked solutions.
- The length of the latus rectum of the parabola 169 (x - 1)^2 + (y - 3)^2 = (5x - 12y + 17)^2 is
- The length of the latus rectum of the parabola x = ay^2 + by + c is
- The parametric equation of a parabola is x = t^2 + 1, y = 2t + 1. The Cartesian equation of its directrix is
- If (2, -8) is at an end of a focal chord of the parabola y^2 = 32x then the other end of the chord is
- A line L passing through the focus of the parabola y^2 = 4(x - 1) intersects the parabola in two distinct points. If m be the...
- The HM of the segments of a focal chord of the parabola y^2 = 4ax is
- The length of a focal chord of the parabola y^2 = 4ax at a distance b from the vertex is c. Then
- The parabola y^2 = kx makes an intercept of length 4 on the line x - 2y = 1. Then k is
- A double ordinate of the parabola y^2 = 8px is of length 16p. The angle subtended by it at the vertex of the parabola is
- The chord AB of the parabola y^2 = 4ax cuts the axis of the parabola at C. If A = (at_1^2, 2at_1), B = (at_2^2, 2at_2) and AC :...
- AB is a chord of the parabola y^2 = 4ax. If its equation is y = mx + c and it subtends a right angle at the vertex of the...
- If t_1 and t_2 are the ends of a focal chord of the parabola y^2 = 2x then
- The equation of a parabola is y^2 = 4x. P(1, 3) and Q(1, 1) are two points in the x-y plane. Then, for the parabola
- The ends of a line segment are P(1, 3) and Q(1, 1). R is a point on the line segment PQ such that PR : QR = 1 : . If R is an...
- The number of distinct real tangents that can be drawn from (0, -2) to the parabola y^2 = 4x is
- The tangents to the parabola y^2 = 4x at the points (1, 2) and (4, 4) meet on the line
- The point of intersection of the tangents to the parabola y^2 = 4x at the points where the parameter t has the value 1 and 2, is
- The triangle formed by the tangents to a parabola y^2 = 4ax at the ends of the latus rectum and the double ordinate through the...
- If two tangents drawn from the point ( , ) to the parabola y^2 = 4x be such that the slope of one tangent is double of the other...
- The tangents from the origin to the parabola y^2 + 4 = 4x are inclined at
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