If tangents are drawn to `y^2=4a x` from any point `P` on the parabola `y^2=a(x+b),` then show that the normals drawn at their point for contact meet on a fixed line.

Tangent are drawn from the point (-1,2) on the parabola y^2=4x . Find the length that these tangents will intercept on the line x=2.

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.

If the two tangents drawn from a point P to the parabola y^(2) = 4x are at right angles then the locus of P is

If normal are drawn from a point P(h , k) to the parabola y^2=4a x , then the sum of the intercepts which the normals cut-off from the axis of the parabola is

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 angle between a pair of tangents drawn from a point P to the hyperbola y^2 = 4ax is 45^@ . Show that the locus of the point P is hyperbola.

If normals drawn at three different point on the parabola y^(2)=4ax pass through the point (h,k), then show that h hgt2a .

Tangents are drawn to x^(2)+y^(2)=1 from any arbitrary point P on the line 2x+y-4=0 .Prove that corresponding chords of contact pass through a fixed point and find that point.

Tangent is drawn at any point (x_1, y_1) other than the vertex on the parabola y^2=4a x . If tangents are drawn from any point on this tangent to the circle x^2+y^2=a^2 such that all the chords of contact pass through a fixed point (x_2,y_2), then (a) x_1,a ,x_2 in GP (b) (y_1)/2,a ,y_2 are in GP (c) -4,(y_1)/(y_2), (x_1//x_2) are in GP (d) x_1x_2+y_1y_2=a^2