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 chord of contact of tangents from a point P to the parabola y^2=4a x touches the parabola x^2=4b y , then the locus of Pdot is a) a cicle b) a parabola c) a straight line d) none of these

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. (a)cuts the given circle orthogonally (b)touches the given circle externally (c)touches the given circle internally (d)none of these

The chords of contact of tangents from three points A ,Ba n dC to the circle x^2+y^2=a^2 are concurrent. Then A ,B and C will (a)be concyclic (b) be collinear (c)form the vertices of a triangle (d)none of these

The chord of contact of tangents from a point P to a circle passes through Q. If l_1 and l_2 are the lengths of the tangents from P and Q to the circle ,then PQ is equal to

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 chord of contact of tangents from a point P to a circle passes through Q, If l_1 and l_2 are the lengths of tangents from P and Q to the circle, then PQ is equal to :

Let A B be chord of contact of the point (5,-5) w.r.t the circle x^2+y^2=5 . Then find the locus of the orthocentre of the triangle P A B , where P is any point moving on the circle.

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 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