Parabola questions
264 published questions with worked solutions.
- Let P(x_1, y_1) and Q(x_2, y_2), y_1 < 0, y_2 < 0, be the end points of the latus rectum of the ellipse x^2 + 4y^2 = 4. The...
- Given : A circle, 2x^2 + 2y^2 = 5 and a parabola, y^2 = 4 5 x. Statement-I : An equation of a common tangent to these curves is y...
- Let one end of a focal chord of the parabola y^2 = 16x be (16, 16). If P( , ) divides this focal chord internally in the ratio...
- If the chord joining the points P_1(x_1, y_1) and P_2(x_2, y_2) on the parabola y^2 = 12x subtends a right angle at the vertex of...
- Let A be the focus of the parabola y^2 = 8x. Let the line y = mx+c intersect the parabola at two distinct points B and C. If the...
- Let P(4, 4 3 ) be a point on the parabola y^2 = 4ax and PQ be a focal chord of the parabola. If M and N are the foot of...
- Let the shortest distance from (a, 0), a > 0, to the parabola y^2 = 4x be 4. Then the equation of the circle passing through the...
- If the line 3x – 2y + 12 = 0 intersects the parabola 4y = 3x^2 at the points A and B, then at the vertex of the parabola, the...
- If the equation of the parabola with vertex V ( 3 2 ,3 ) and the directrix x + 2y = 0 is x^2 + y^2 - xy - 30x - 60y + 225 = 0,...
- Let ABCD be a trapezium whose vertices lie on the parabola y^2 = 4x. Let the sides AD and BC of the trapezium be parallel to...
- Let the ellipse, E_1 : x^2 a^2 + y^2 b^2 = 1, a > b and E_2 : x^2 A^2 + y^2 B^2 = 1, A < B have same eccentricity 1 3 . Let the...
- Let y^2=12x the parabola and S be its focus. Let PQ be a focal chord of the parabola such that (SP)(SQ)= 147 4 . Let C be the...
- Let the point P of the focal chord PQ of the parabola y^2 = 16x be (1, –4). If the focus of the parabola divides the chord PQ in...
- The slope of the line touching both the parabolas y^2 = 4x and x^2 = -32y is
- If the tangent at (1, 7) to the curve x^2 = y - 6 touches the circle x^2 + y^2 + 16x + 12y + c = 0 then the value of c is:
- Tangent and normal are drawn at P(16, 16) on the parabola y^2 = 16x, which intersect the axis of the parabola at A and B,...
- The tangent to the parabola y^2 = 4x at the point where it intersects the circle x^2 + y^2 = 5 in the first quadrant, passes...
- If one end of a focal chord of the parabola, y^2 = 16x is at (1, 4), then the length of this focal chord is:
- Two parabolas with a common vertex and with axes along x-axis and y-axis, respectively, intersect each other in the first...
- Tangents drawn from the point (–8, 0) to the parabola y^2 = 8x touch the parabola at P and Q. If F is the focus of the parabola,...
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