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.

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+3=0 parabola y^(2)=8x. Then the variable chords of contact pass through a fixed point whose coordinates are (A) (3,2)(B)(2,4) (C) (3,4) (D) (4,1)

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 (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 .