Parabola questions
264 published questions with worked solutions.
- The parabolas ax^2+2bx+cy=0 and dx^2+2ex+fy=0 intersect on the line y=1. If a,b,c,d,e,f are positive real numbers and a,b,c are...
- A tangent and a normal are drawn at the point P(2, –4) on the parabola y^2=8x, which meet the directrix of the parabola at the...
- If two tangents drawn from a point P to the parabola y^2=16(x-3) are at right angles, then the locus of point P is :
- A line is a common tangent to the circle (x-3)^2+y^2=9 and the parabola y^2=4x. If the two points of contact (a, b) and (c, d)...
- A tangent is drawn to the parabola y^2=6x which is perpendicular to the line 2x + y = 1. Which of the following points does NOT...
- Let a parabola P be such that its vertex and focus lie on the positive x–axis at a distance 2 and 4 units from the origin,...
- If two tangents drawn from a point ( , ) lying on the ellipse 25x^ 2 + 4y^ 2 = 1 to the parabola y^ 2 = 4x are such that the...
- A particle is moving in the xy-plane along a curve C passing through the point (3, 3). The tangent to the curve C at the point P...
- If t_1 and t_2 are roots of the equation t^2+ t+1=0, where is an arbitrary constant. Then, the line joining the points...
- The tangents at the points A(1, 3) and B(1, −1) on the parabola y^ 2 - 2x - 2y = 1 meet at the point P. Then the area (in unit^ 2...
- The sum of diameters of the circles that touch (i) the parabola 75x^ 2 = 64(5y - 3) at the point (8/5, 6/5) and (ii) the y-axis,...
- If y = m_ 1 x + c_ 1 and y = m_ 2 x + c_ 2 , m_ 1 m_ 2 are two common tangents of circle x^ 2 + y^ 2 = 2 and parabola y^ 2 = x,...
- The equation of a common tangent to the parabolas y = x^ 2 and y = −(x − 2)^ 2 is
- Let the tangent drawn to the parabola y^ 2 = 24x at the point ( , ) is perpendicular to the line 2x + 2y = 5. Then the normal to...
- A tangent line L is drawn at the point (2 –4) on the parabola y^2=8x. If the line L is also tangent to the circle x^2+y^2=a, then...
- If the x-intercept of a focal chord of the parabola y^2=8x+4y+4 is 3, then the length of the chord is equal to __________.
- 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 (x, y) be any point on the parabola y^2 = 4x. Let P be the point that divides the line segment from (0, 0) to (x, y) in the...
- Let L be a normal to the parabola y^2 = 4x. If L passes through the point (9, 6), then L is given by
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