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.

Tangents PA and PB are drawn to the circle x^2 +y^2=8 from any arbitrary point P on the line x+y =4 . The locus of mid-point of chord of contact AB is

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

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 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 the hyperbola x^(2)/9 - y^(2)/4 parallel to the straight line 2x - y= 1 . One of the points of contact of tangents on the hyperbola is

The normal to the curve y(x-2)(x-3)=x+6 at the point where the curve intersects the y-a xi s , passes through the point : (1/2,-1/3) (2) (1/2,1/3) (3) (-1/2,-1/2) (4) ((1/(2,1))/2)

Tangents are drawn from the point P(3, 4) to the ellipse x^2/9+y^2/4=1 touching the ellipse at points A and B.

The chords of contact of the pair of tangents drawn from each point on the line 2x + y=4 to the circle x^2 + y^2=1 pass through the point (a,b) then 4(a+b) is