Two lines are drawn at right angles, one being a tangent to `y^2=4a x` and the other `x^2=4b ydot` Then find the locus of their point of intersection.

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

Tangents are drawn at the end points of a normal chord of the parabola y^(2)=4ax . The locus of their point of intersection is

Tangents are drawn from points of the parabola y^(2)=4ax to the parabola y^(2)=4b(x-c) . Find the locus of the mid point of chord of contact.

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

Find the angle between the parabolas y^2=4a x and x^2=4b y at their point of intersection other than the origin.

Two straight lines are perpendicular to each other. One of them touches the parabola y^2=4a(x+a) and the other touches y^2=4b(x+b) . Their point of intersection lies on the line. x-a+b=0 (b) x+a-b=0 x+a+b=0 (d) x-a-b=0

If the tangents to the parabola y^(2)=4ax intersect the hyperbola (x^(2))/(a^(2))-(y^(2))/(b^(2))=1 at A and B, then find the locus of the point of intersection of the tangents at A and B.

Chords of the hyperbola x^2/a^2-y^2/b^2=1 are tangents to the circle drawn on the line joining the foci asdiameter. Find the locus of the point of intersection of tangents at the extremities of the chords.