Parabola questions
264 published questions with worked solutions.
- The equation of the parabola with vertex (-1, 1) and focus (2, 1) is
- The curve described parametrically by x = t^2 + 2t - 1, y = 3t + 5 represents
- The focal distance of a point P on the parabola y^2 = 12x, if the ordinate of P is 6, is
- If the straight line lx + my + n = 0 touches the parabola, y^2 = 4ax, then
- The value of c, for which the line y = 2x + c, is tangent to the parabola y^2 = 4a(x + a), is
- If two tangents drawn from a point P to the parabola y^2 = 4x are at right angles, then the locus of P is
- If b and C are the lengths of the segments of any focal chord of a parabola y^2 = 4ax, then the length of the semilatusrectum is
- The tangent at (1, 7) to the curve x^2 = y - 6 touches the circle x^2 + y^2 + 16x + 12y + c = 0 at
- In the parabola, y^2=x, what is the length of the chord passing through the vertex and inclined to the x-axis at an angle ?
- What is the equation of the parabola with focus (-3, 0) and directrix x-3=0?
- What is the equation of directrix of parabola y^2=4bx, where b<0 and b^2+b-2=0?
- In the parabola y^2=8x, the focal distance of a point P lying on it is 8 units. Which of the following statements is/are correct?...
- Consider the points P(4k, 4k) and Q(4k, -4k) lying on the parabola y^2=4kx. If the vertex is A, then what is PAQ equal to?
- A tangent to the parabola y^2=4x is inclined at an angle 45^ with the positive direction of x-axis. What is the point of contact...
- Consider the following statements in respect of the equation x^2+3y=0 : I. The equation represents the equation to parabola that...
- What is the eccentricity (e) of the parabola 4x^2+y=0?
- Consider the following with regard to eccentricity (e) of a conic section : 1. e=0 for circle 2. e=1 for parabola 3. e<1 for...
- Let E denote the parabola y^2 = 8x. Let P = (-2, 4), and let Q and Q' be two distinct points on E such that the lines PQ and PQ'...
- Consider the parabola y^2 = 4x. Let S be the focus of the parabola. A pair of tangents drawn to the parabola from the point P =...
- Let T_1 and T_2 be two distinct common tangents to the ellipse E: x^2 6 + y^2 3 = 1 and the parabola P: y^2 = 12x. Suppose that...
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