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`

If the chord of contact of tangents drawn from the (h, k) to the circle x^2+y^2=a^2 subtends a right at the centre, then:

The length of the chord of contact of the tangents drawn from the point (-2,3) to the circle x^2+y^2-4x-6y+12=0 is:

The length of the chord of contact of the tangents drawn from the point (-2,3) to the circle x^2+y^2-4x-6y+12=0 is:

if the chord of contact of tangents from a point P to the hyperbola x^2/a^2-y^2/b^2=1 subtends a right angle at the centre, then the locus of P is

if the chord of contact of tangents from a point P to the hyperbola x^2/a^2-y^2/b^2=1 subtends a right angle at the centre, then the locus of P is

Prove that the chord of contact of tangents drawn from the point (h,k) to the ellipse x^(2)/a^(2)+y^(2)/b^(2)=1 will subtend a right angle at the centre, if h^(2)/a^(4)+k^(2)/b^(4)=1/a^(2)+1/b^(2)

Prove that the chord of contact of tangents drawn from the point (h,k) to the ellipse x^(2)/a^(2)+y^(2)/b^(2)=1 will subtend a right angle at the centre, if h^(2)/a^(4)+k^(2)/b^(4)=1/a^(2)+1/b^(2)

Prove that the chord of contact of tangents drawn from the point (h,k) to the ellipse x^(2)/a^(2)+y^(2)/b^(2)=1 will subtend a right angle at the centre, if h^(2)/a^(4)+k^(2)/b^(4)=1/a^(2)+1/b^(2)

Chord of contact of tangents drawn from the point M(h, k) to the ellipse x^(2) + 4y^(2) = 4 intersects at P and Q, subtends a right angle of the centre theta

Find the condition that the chord of contact of tangents from the point (alpha, beta) to the circle x^2 + y^2 = a^2 should subtend a right angle at the centre. Hence find the locus of (alpha, beta) .