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`.

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.

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

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.

Tangents are drawn from any point on the circle x^(2)+y^(2) = 41 to the ellipse (x^(2))/(25)+(y^(2))/(16) =1 then the angle between the two tangents is

Tangents are drawn from the point (-1, 2) to the parabola y^2 =4x The area of the triangle for tangents and their chord of contact is

Tangents are drawn from the point (-1, 2) to the parabola y^2 =4x The area of the triangle for tangents and their chord of contact is

PA and PB are tangents drawn from a point P to the ellipse (x^2)/(a^2)+(y^2)/(b^2)=1 . The area of the triangle formed by the chord of contact AB and axes of co-ordinates is constant. Then locus of P is:

If tangents are drawn from any point on the circle x^(2) + y^(2) = 25 the ellipse (x^(2))/(16) + (y^(2))/(9) =1 then the angle between the tangents is

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

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