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`

The equation of tangents drawn from the origin to the circle x^2+y^2-2rx-2hy+h^2=0

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.

Find the locus of the midpoint of the chords of the circle x^2+y^2=a^2 which subtend a right angle at the point (0,0)dot

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 two tangents drawn from a point P to the parabola y^(2) = 4x are at right angles then the locus of P is

If the length tangent drawn from the point (5, 3) to the circle x^2+y^2+2x+k y+17=0 is 7, then find the value of kdot

If two tangents drawn from the point (alpha,beta) to the parabola y^2=4x are such that the slope of one tangent is double of the other, then prove that alpha=2/9beta^2dot

Statement 1 : If the chords of contact of tangents from three points A ,Ba n dC to the circle x^2+y^2=a^2 are concurrent, then A ,Ba n dC will be collinear. Statement 2 : Lines (a_1x+b_1y+c_1)+k(a_2x+b_2y+c_2)=0 alwasy pass through a fixed point for k in R .

If the chords of contact of tangents from two poinst (x_1, y_1) and (x_2, y_2) to the ellipse (x^2)/(a^2)+(y^2)/(b^2)=1 are at right angles, then find the value of (x_1x_2)/(y_1y_2)dot