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)

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^(2)

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) .

If the chords of contact of tangents from two points (-4,2) and (2,1) to the hyperbola (x^(2))/(a^(2))-(y^(2))/(b^(2))=1 are at right angle, then find then find the eccentricity of the hyperbola.

The equation of the chord of contact of tangents from (1,2) to the hyperbola 3x^(2)-4y^(2)=3 , is

If the chords of contact of tangents drawn from P to the hyperbola x^(2)-y^(2)=a^(2) and its auxiliary circle are at right angle, then P lies on

If the chord of contact of tangents from a point P(h, k) to the circle x^(2)+y^(2)=a^(2) touches the circle x^(2)+(y-a)^(2)=a^(2) , then locus of P is