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 (a)conjugate hyperbola (b)one of the directrix (c)one of the asymptotes (d) none of these

Four points are such that the line joining any two points is perpendicular to the line joining other two points. If three points out of these lie on a rectangular hyperbola, then the fourth point will lie on the saem hyperbola the conjugate hyperbola one of the directrix one of the asymptotes

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.

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

The chord of contact of tangents from a point P to a circle passes through Qdot If l_1a n dl_2 are the length of the tangents from Pa n dQ to the circle, then P Q 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 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 ,Ba n dC will (a)be concyclic (b) be collinear (c)form the vertices of a triangle (d)none of these

The angle between a pair of tangents drawn from a point P to the hyperbola y^2 = 4ax is 45^@ . Show that the locus of the point P is hyperbola.

The locus of the foot of perpendicular from my focus of a hyperbola upon any tangent to the hyperbola is the auxiliary circle of the hyperbola. Consider the foci of a hyperbola as (-3, -2) and (5,6) and the foot of perpendicular from the focus (5, 6) upon a tangent to the hyperbola as (2, 5). The point of contact of the tangent with the hyperbola is

If alpha+beta=3pi , then the chord joining the points alpha and beta for the hyperbola (x^2)/(a^2)-(y^2)/(b^2)=1 passes through which of the following points? (a)Focus (b) Center (c)One of the endpoints of the transverse exis. (d)One of the endpoints of the conjugate exis.

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.