Two tangents to the parabola `y^(2)=4ax` meet at an angle `alpha`. Prove that the locus of their of intersections, is `y^(2)-4ax=(x+a)^(2) tan^(2) alpha`

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 slope of the tangent to the parabola y^(2)=4ax at the point (at^(2), 2at) is -

PQ is a chord of the parabola y^(2) = 4ax . The ordinate of P is twice that of Q . Prove that the locus of the mid - point of PQ is 5y^(2) = 18 ax

If a tangent to the parabola y^2 = 4ax intersects the x^2/a^2+y^2/b^2= 1 at A and B , then the locus of the point of intersection of tangents at A and B to the ellipse is

A pair of tangents are drawn to the parabola y^2=4a x which are equally inclined to a straight line y=m x+c , whose inclination to the axis is alpha . Prove that the locus of their point of intersection is the straight line y=(x-a)tan2alphadot

bar(PQ) is a double ordinate of the parabola y^2=4ax ,find the equation to the locus of its point of trisection.

PQ is a double ordinate of the parabola y^2=4ax Show that thelocus of its point of trisection the chord PQ is 9y^2=4ax .

y=x is tangent to the parabola y=ax^(2)+c . If a=2, then the value of c is

overline(PQ) is a double ordinate of the parabola y^(2) = 4ax ,find the equation to the locus of its point of trisection .

The angle between tangents to the parabola y^2=4ax at the points where it intersects with teine x-y-a = 0 is (a> 0)