The chord of contact of a point `P` w.r.t a hyperbola and its auxiliary circle are at right angle. Then the point `P` lies on conjugate hyperbola one of the directrix one of the asymptotes (d) none of these

The chord of contact of a point P w.r.t a hyperbola and its auxiliary circle are at right angle. Then the point P lies (a) on conjugate hyperbola (b) one of the directrix (c) one of the asymptotes (d) none of these

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

Let P be any point on any directrix of an ellipse. Then the chords of contact of point P with respect to the ellipse and its auxiliary circle intersect at (a)some point on the major axis depending upon the position of point Pdot (b)the midpoint of the line segment joining the center to the corresponding focus (c)the corresponding focus (d)none of these

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

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 the chord of contact of tangents from a point P to a given circle passes through Q , then the circle on P Q as diameter. cuts the given circle orthogonally touches the given circle externally touches the given circle internally none of these

If x= 9 is a chord of contact of the hyperbola x^(2) -y^(2) =9 , then the equation of the tangents at one of the points of contact is

In a hyperbola, the portion of the tangent intercepted between the asymptotes is bisected at the point of contact. Consider a hyperbola whose center is at the origin. A line x+y=2 touches this hyperbola at P(1,1) and intersects the asymptotes at A and B such that AB = 6sqrt2 units. The equation of the tangent to the hyperbola at (-1, 7//2) is

In a hyperbola, the portion of the tangent intercepted between the asymptotes is bisected at the point of contact. Consider a hyperbola whose center is at the origin. A line x+y=2 touches this hyperbola at P(1,1) and intersects the asymptotes at A and B such that AB = 6sqrt2 units. The equation of the pair of asymptotes is