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,...
- Let S be the set of all a N such that the area of the triangle formed by the tangent at the point P(b, c), b, c N, on the...
- Let y = f(x) represent a parabola with focus (- 1 2 ,0 ) and directrix y = - 1 2 . Then S = x R: ^ -1 ( f(x) )+ ^ -1 ( f(x)+1 )=...
- STATEMENT-1 : The curve y = -x^2 2 + x + 1 is symmetric with respect to the line x = 1. because STATEMENT-2 : A parabola is...
- 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...
- Two common tangents to the circle x^2 + y^2 = 2a^2 and parabola y^2 = 8ax are
- The normal at the point (bt_1^2, 2bt_1 ) on a parabola meets the parabola again in the point (bt_2^2, 2bt_2 ), then
- The locus of the vertices of the family of parabolas y = a^3x^2 3 + a^2x 2 - 2a is
- The equation of a tangent to the parabola y^2 = 8x is y = x + 2. The point on this line from which the other tangent to the...
- A parabola has the origin as its focus and the line x = 2 as the directrix. Then the vertex of the parabola is at
- If two tangents drawn from a point P to the parabola y^2 = 4x are at right angles, then the locus of P is
- The distance of the focus of the parabola y^2=16x from its directrix is
- The area of the triangle formed by the lines joining the vertex of the parabola x^2=48y to the ends of its latus rectum, 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 tangent to the parabola y^ 2 =8x, which is parallel to the line 4x-y+3=0 is
- A parabola has its focus on the positive X-axis and the Y-axis as its directrix. If P( , 4) is a point on this parabola such that...
- The area of the triangle formed by the lines joining the vertex of the parabola x^2 = 20y to the end of its Latus rectum is
- The Y-intercept of the common tangent to the parabola y^2 = 32x and x^2 = 108y is
- The line y=mx+3 is tangent to the parabola y^ 2 =4x, if the value of m is
- The equation of the directrix of the parabola y^2+4y+4x+2=0 is
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