Tangent is drawn at any point `(x_1,y_1)` on the parabola `y^2=4ax` . Now 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 throught a fixed point `(x_2,y_2)` Prove that `4(x_1/x_2)+(y_1/y_2)^2=0`.

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

Tangent is drawn at any point (p,q) on the parabola y^(2)=4ax. Tangents are drawn from any point on this tangant to the circle x^(2)+y^(2)=a^(2), such that the chords of contact pass through a fixed point (r,s). Then p,q,r ands through a fixed point (r,s). Then p,q,rrq^(2)=4ps^(2)( C) rq^(2)=-4ps^(2)(D)r^(2)q=-4p^(2)s

tangent is drawn at point P(x_(1),y_(1)) on the hyperbola (x^(2))/(4)-y^(2)=1. If pair of tangents are drawn from any point on this tangent to the circle x^(2)+y^(2)=16 such that chords of contact are concurrent at the point (x_(2),y_(2)) then

Tangents are drawn from the points on the line x-y-5=0 ot x^(2)+4y^(2)=4 . Prove that all the chords of contanct pass through a fixed point

Tangents are drawn from points on the line x-y+2=0 to the ellipse x^(2)+2y^(2)=4 then all the chords of contact pass through the point

Tangents are drawn from the points on the line x-y-5=0 to x^(2)+4y^(2)=4. Then all the chords of contact pass through a fixed point. Find the coordinates.