A line intesects the ellipse (x^(2))/(4a...

A line intesects the ellipse `(x^(2))/(4a^(2))+(y^(2))/(a^(2))=1` at A and B and the parabola `y^(2)=4a(x+2a)` at C and D. The line segment AB substends a right angle at the centre of the ellipse. Then, the locus of the point of intersection of tangents to the parabola at C and D, is

Verified by Experts

The correct Answer is:

`y^(2)+4d^(2)=4d^(2)(x+2a)^(2)((1)/(a^(2))+(1)/(b^(2)))`

Similar Questions

Explore conceptually related problems

The locus of the point of intersection of perpendicular tangents to the parabola y^(2)=4ax is

The locus of the point of intersection of the perpendicular tangents to the parabola x^2=4ay is .

The locus of point of intersection of perpendicular tangent to parabola y^2= 4ax

The locus of point of intersection of tangents inclined at angle 45^@ to the parabola y^2 = 4x is

The locus of pole of tangents to the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1 with respect to the parabola y^(2)=4ax, is

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

The locus of the intersection points of pair of perpendicular tangents to the parabola x^2-4x + 4y-8=0 . is

The line 2x+y=3 intersects the ellipse 4x^(2)+y^(2)=5 at two points. The point of intersection of the tangents to the ellipse at these point is

The locus of the point of intersection of two prependicular tangents of the ellipse x^(2)/9+y^(2)/4=1 is

Prove that the tangents drawn on the parabola y^(2)=4ax at points x = a intersect at right angle.