Home
Class 12
MATHS
If parabola of latus rectum touches a fi...

If parabola of latus rectum touches a fixed equal parabola, the axes of the two curves being parallel, then the locus of the vertex of the moving curve is

Text Solution

Verified by Experts

The correct Answer is:
`y^2=8ax`
Promotional Banner

Similar Questions

Explore conceptually related problems

Let two paraboles have a common axis where focus of each being exterior to the other and lt l_(1),l_(2) be their latus rectums then the locus of the mid points of the intercepts between the parabolas made on the lines parallel to the common axis is a

If from the vertex of a parabola y^2=4x a pair of chords be drawn at right angles to one another andwith these chords as adjacent sides a rectangle be made, then the locus of the further end of the rectangle is

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 as its diameter, then the slope of the line joining A and B can be (A) - 1/r (B) 1/r (C) 2/r (D) - 2/r

Prove that the semi-latus rectum of the parabola 'y^2 = 4ax' is the harmonic mean between the segments of any focal chord of the parabola.

If a tangent to the parabola y^2 = 4ax meets the axis of the parabola in T and the tangent at the vertex A in Y, and the rectangle TAYG is completed, show that the locus of G is y^2 + ax = 0.

Two tangents to the parabola y^2=4ax make supplementary angles with the x-axis. Then the locus of their point of intersection is

Prove that the equation y^2+2ax+2by+c=0 represent a parabola whose axis is parallel to the axis of x. Find its vertex.

If on a given base B C , a triangle is described such that the sum of the tangents of the base angles is m , then prove that the locus of the opposite vertex A is a parabola.

If the normals at two points P and Q of a parabola y^2 = 4ax intersect at a third point R on the curve, then the product of ordinates of P and Q is