Parabola questions
264 published questions with worked solutions.
- Let P be a point whose coordinates differ by unity and the point does not lie on any of the axes of reference. If the parabola...
- Let AB be a chord of the parabola y^2 = 4ax. If the pole of AB with respect to the parabola be (2a, 3a) then the length of AB is
- The vertex of the parabola x^2 = 2(2x + y) is
- The equation of a common tangent to the circle x^2 + y^2 = 2a^2 and the parabola y^2 = 8ax is
- Normals are drawn from the point P with slopes m_1, m_2, m_3 to the parabola y^2 = 4x. If the locus of P when m_1m_2 = k is part...
- Two tangents to the parabola x^2 = 6y meet at the point (-1, - 32 ). STATEMENT-1: The tangents are perpendicular to each other....
- The line x - 1 = 0 is the directrix of the parabola y^2 - kx + 8 = 0. Then one of the values of k is
- The equation of the common tangent touching the circle (x-3)^2 + y^2 = 9 and the parabola y^2 = 4x above the x-axis, is
- The equation of the directrix of the parabola y^2 + 4y + 4x + 2 = 0 is
- The equations of common tangents to the parabolas y = x^2 and y = -(x-2)^2 are
- Normals are drawn at points P, Q and R lying on the parabola y^2 = 4x and they intersect at (3, 0). Then Column I: (i) Area of...
- The equation of the common tangent to the curves y^2 = 8x and xy = -1 is
- The axis of a parabola is along the line y = x and the distance of the origin from its vertex is 2 and that from its focus is 2...
- STATEMENT-1: The curve y = -x^2 2 + x + 1 is symmetric with respect to the line x = 1. STATEMENT-2: A parabola is symmetric about...
- Let P(x_1, y_1) and Q(x_2, y_2); where y_1 < 0, y < 0 be the end points of the latus rectum of the ellipse x^2 + 4y^2 = 4. The...
- The tangent PT and the normal PN to the parabola y^2 = 4ax at a point P on it meet its axis at points T and N respectively. The...
- Match the conic sections in Column I with the statements/expressions in Column II. Column I: (A) Circle (B) Parabola (C) Ellipse...
- Let A and B be two distinct points on the parabola y^2 = 4x. If the axis of the parabola touches a circle of radius r having AB...
- Consider the parabola y^2 = 8x. Let _1 be the area of the triangle formed by the end points of its latus rectum and the point P (...
- Let O be the vertex and Q be any point on the parabola, x^2 = 8y. If the point P divides the line segment OQ internally in the...
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