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`

If chords of contact of the tangent from two points (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 (x_1x_2)/(y_1y_2) is equal to

If the chords of contact of tangents fromtwo points (x_(1),y_(1)) and (x_(2),y_(2)) to the hyperbola (x^(2))/(a^(2))-(y^(2))/(b^(2))=1 are at right angles,then (x_(1)x_(2))/(y_(1)y_(2)) is equal to (a) (a^(2))/(-b^(2))( b) (b^(2))/(-a^(2))( c) (b^(4))/(-a^(4))

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.

If chord of contact of the tangent drawn from the point (a,b) to the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1 touches the circle x^(2)+y^(2)=k^(2), then find the locus of the point (a,b).