If the chord `xcosalpha+ysinalpha=p` of the hyperbola `(x^2)/(16)-(y^2)/(18)=1` subtends a right angle at the center, and the diameter of the circle, concentric with the hyperbola, to which the given chord is a tangent is `d ,` then the value of `d/4` is__________

The condition that the chord xcosalpha+ysinalpha-p=0 of x^2+y^2-a^2=0 may subtend a right angle at the center of the circle is

A normal chord of the parabola y^2=4ax subtends a right angle at the vertex if its slope is

A variable chord of the hyperbola (x^2)/(a^2)-(y^2)/(b^2)=1,(b > a), subtends a right angle at the center of the hyperbola if this chord touches. a fixed circle concentric with the hyperbola a fixed ellipse concentric with the hyperbola a fixed hyperbola concentric with the hyperbola a fixed parabola having vertex at (0, 0).

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.

With one focus of the hyperbola x^2/9-y^2/16=1 as the centre, a circle is drawn which is tangent to the hyperbola with no part of the circle being outside the hyperbola. The radius of the circle is

If P Q is a double ordinate of the hyperbola (x^2)/(a^2)-(y^2)/(b^2)=1 such that O P Q is an equilateral triangle, O being the center of the hyperbola, then find the range of the eccentricity e of the hyperbola.

If the chord y=m x+1 of the circles x^2+y^2=1 subtends an angle of 45^0 at the major segment of the circle, then the value of m is

If the chord of contact of the tangents drawn from the point (h , k) to the circle x^2+y^2=a^2 subtends a right angle at the center, then prove that h^2+k^2=2a^2dot

If the latus rectum subtends a right angle at the center of the hyperbola (x^2)/(a^2)-(y^2)/(b^2)=1 , then find its eccentricity.

If A ,B ,a n dC are three points on the hyperbola x y=c^2 such that A B subtends a right angle at C , then prove that A B is parallel to the normal to the hyperbola at point Cdot