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 from any point on the hyperbola (x^2)/9-(y^2)/4=1 to the circle x^2+y^2=9 . Find the locus of the midpoint of the chord of contact.

The tangents from (alpha, beta) to the ellipse x^2/a^2 + y^2/b^2 = 1 intersect at right angle. Show that the locus of the point of intersection of normals at the point of contact of the two tangents is the line ay-betax=0 .

Find the locus of the point of intersection of the perpendicular tangents of the curve y^2+4y-6x-2=0 .

Find the locus of the point of intersection of the perpendicular tangents of the curve y^2+4y-6x-2=0 .

Find the locus of the point of intersection of perpendicular tangents to the circle x^(2) + y^(2)= 4

If two tangents are drawn from a point to the circle x^(2) + y^(2) =32 to the circle x^(2) + y^(2) = 16 , then the angle between the tangents is

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

Tangents are drawn from a point on the ellipse x^2/a^2 + y^2/b^2 = 1 on the circle x^2 + y^2 = r^2 . Prove that the chord of contact are tangents of the ellipse a^2 x^2 + b^2 y^2 = r^4 .

Find the locus of the point of intersections of perpendicular tangents to the circle x^(2) +y^(2) =a^(2)

If tangents be drawn from points on the line x=c to the parabola y^2=4x , show that the locus of point of intersection of the corresponding normals is the parabola.