If the chords of contact of tangents from two points to the ellipse are a right angles, then show that `(x_(1)x_(2))/(y_(1)y_(2))=-(a^(4))/(b^(4))`

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

The points of contact of the tangents drawn from the point (4, 6) to the parabola y^(2) = 8x

The point of contact of the tangents drawn from origin to the curve y=x^2+3x+4 is

The slopes of the tangents drawn from (4, 1) to the ellipse x^(2)+2y^(2)=6 are

If the chords of contact of tangents from two points (x_(1),y_(1)) and (x_(2),y_(2)) to the hyperola x^(2)/a^(2)-y^(2)/b^(2)=1 are at right angles, then find (x_(1)x_(2))/(y_(1)y_(2))

Let d be the perpendicular distance from the centre of the ellipse x^(2)/a^(2)+y^(2)/b^(2) = 1 to the tangent drawn at a point P on ellipse. If F_(1) and F_(2) are the foci of the ellipse, then show that (PF_(1)-PF_(2))^(2)=4a^(2)(1-(b^(2))/(d^(2)))

If the chords of contact of P(x_(1),y_(1)) and Q(x_(2)_,y_(2)) w.r.t the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1 are right angle then (x_(1)x_(2))/(y_(1)y_(2)) =