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 from any point on the conic x^2/a^2 + y^2/b^2 = 4 to the conic x^2/a^2 + y^2/b^2 = 1 . Find the locus of the point of intersection of the normals at the point of contact of the two tangents.

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

If the tangents to the parabola y^2=4a x intersect the hyperbola (x^2)/(a^2)-(y^2)/(b^2)=1 at Aa n dB , then find the locus of the point of intersection of the tangents at Aa n dBdot

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.

Find the angle of intersection of the curves y^2=4a x and x^2=4b y .

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

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.

Find the area included between the parabolas y^2=4a x\ a n d\ x^2=4b ydot