Locus of mid-points of chords of the hyperbola `(x^(2))/(a^(2))-(y^(2))/(b^(2))=1` ,such angle between tangents at the end of the chords is `90^(@)` is:

The locus of mid-points of a focal chord of the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1

The locus of the poles of the chords of the hyperbola (x^(2))/(a^(2))-(y^(2))/(b^(2))=1 which subtend a right angle at its centre is

Find the locus of the mid-points of normal chords of the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1

Locus of mid-point of the focal chord of ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1 with eccentricity e is

The locus of the mid-points of the chords of the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1 which pass through the positive end of major axis,is.

Prove that the locus of the middle-points of the chords of the hyperbola (x^(2))/(a^(2))-(y^(2))/(b^(2))=1 which pass through a fixed point (alpha, beta) is a hyperbola whose centre is ((alpha)/(2), (beta)/(2)) .

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