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.

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 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 .

Tangent are drawn from the point (3, 2) to the ellipse x^2+4y^2=9 . Find the equation to their chord of contact and the middle point of this chord of contact.

From the origin, chords are drawn to the circle (x-1)^2 + y^2 = 1 . The equation of the locus of the mid-points of these chords

If from the origin a chord is drawn to the circle x^(2)+y^(2)-2x=0 , then the locus of the mid point of the chord has equation

Tangents are drawn from the points on a tangent of the hyperbola x^2-y^2=a^2 to the parabola y^2=4a xdot If all the chords of contact pass through a fixed point Q , prove that the locus of the point Q for different tangents on the hyperbola is an ellipse.

Tangents are drawn from a point P to the hyperbola x^2/2-y^2= 1 If the chord of contact is a normal chord, then locus of P is the curve 8/x^2 - 1/y^2 = lambda where lambda in N .Find lambda

The tangent at any point P on the circle x^2+y^2=4 meets the coordinate axes at A and B . Then find the locus of the midpoint of A Bdot

Tangents drawn from a point on the circle x^2+y^2=9 to the hyperbola x^2/25-y^2/16=1, then tangents are at angle

Tangents are drawn from any point on the line x+4a=0 to the parabola y^2=4a xdot Then find the angle subtended by the chord of contact at the vertex.