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 to x^(2)+4y^(2)=4 . Prove that all the chords of contact pass through a fixed 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

Tangents are drawn to x^2+y^2=1 from any arbitrary point P on the line 2x+y-4=0 . The corresponding chord of contact passes through a fixed point whose coordinates are (1/2,1/2) (b) (1/2,1) (1/2,1/4) (d) (1,1/2)

If the tangents are drawn from any point on the line x+y=3 to the circle x^2+y^2=9 , then the chord of contact passes through the point. a)(3, 5) (b) (3, 3) (c) (5, 3) (d) none of these

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 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 any point on the line (t+2)(x+y) =1, t ne -2 , tangents are drawn to the ellipse 4x^(2)+16y^(2) = 1 . It is given that chord of contact passes through a fixed point. Then the number of integral values of 't' for which the fixed point always lies inside the ellipse is

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.

A variable circle which always touches the line x+y-2=0 at (1, 1) cuts the circle x^2+y^2+4x+5y-6=0 . Prove that all the common chords of intersection pass through a fixed point. Find that points.

Show that all chords of the curve 3x^2-y^2-2x+4y=0, which subtend a right angle at the origin, pass through a fixed point. Find the coordinates of the point.