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

If the chord of contact of the tangents drawn from a point on the circle x^2+y^2=a^2 to the circle x^2+y^2=b^2 touches the circle x^2+y^2=c^2 , then prove that a ,b and c are in GP.

Equation of the smaller circle that touches the circle x^2+y^2=1 and passes through the point (4,3) is

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

If the chord of contact of the tangents drawn from the point (h , k) to the circle x^2+y^2=a^2 subtends a right angle at the center, then prove that h^2+k^2=2a^2dot

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.

A point P moves such that the chord of contact of the pair of tangents from P on the parabola y^2=4a x touches the rectangular hyperbola x^2-y^2=c^2dot Show that the locus of P is the ellipse (x^2)/(c^2)+(y^2)/((2a)^2)=1.

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.

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

The locus of the mid-point of the chord of contact of tangents drawn from points lying on the straight line 4x-5y=20 to the circle x^2+y^2=9 is : (A) 20(x^2+y^2)-36+45y=0 (B) 20(x^2+y^2)+36-45y=0 (C) 20(x^2+y^2)-20x+45y=0 (D) 20(x^2+y^2)+20x-45y=0

If the chord of contact of tangents from a point P to the parabola y^2=4a x touches the parabola x^2=4b y , then find the locus of Pdot