If `S and S''` are the foci, C is the centre, and P is a point on a rectangular hyperbola, show that `SPxxS'P=(CP_(2))`.

If S ans S' are the foci, C is the center , and P is point on the rectangular hyperbola, show that SP ×SP=(CP)^2

Statement 1 : If (3, 4) is a point on a hyperbola having foci (3, 0) and (lambda,0) , the length of the transverse axis being 1 unit, then lambda can take the value 0 or 3. Statement 2 : |S^(prime)P-S P|=2a , where Sa n dS ' are the two foci, 2a is the length of the transverse axis, and P is any point on the hyperbola.

If p ,q ,r ,s are rational numbers and the roots of f(x)=0 are eccentricities of a parabola and a rectangular hyperbola, where f(x)=p x^3+q x^2+r x+s ,then p+q+r+s= a. p b. -p c. 2p d. 0

If P N is the perpendicular from a point on a rectangular hyperbola x y=c^2 to its asymptotes, then find the locus of the midpoint of P N

The vertices of Delta ABC lie on a rectangular hyperbola such that the orthocenter of the triangle is (3, 2) and the asymptotes of the rectangular hyperbola are parallel to the coordinate axes. The two perpendicular tangents of the hyperbola intersect at the point (1, 1). The equation of the rectangular hyperbola is

Let A B C D be a rectangle and P be any point in its plane. Show that A P^2+P C^2=P B^2+P D^2dot

The vertices of Delta ABC lie on a rectangular hyperbola such that the orthocenter of the triangle is (3, 2) and the asymptotes of the rectangular hyperbola are parallel to the coordinate axes. The two perpendicular tangents of the hyperbola intersect at the point (1, 1). The equation of the pair of asymptotes is

P Q and R S are two perpendicular chords of the rectangular hyperbola x y=c^2dot If C is the center of the rectangular hyperbola, then find the value of product of the slopes of C P ,C Q ,C R , and C Sdot

The vertices of Delta ABC lie on a rectangular hyperbola such that the orthocenter of the triangle is (3, 2) and the asymptotes of the rectangular hyperbola are parallel to the coordinate axes. The two perpendicular tangents of the hyperbola intersect at the point (1, 1). The number of real tangents that can be drawn from the point (1, 1) to the rectangular hyperbola is

A point P moves such that the chord of contact of the pair of tangents from P on the parabola y^2=4a x touches the rectangular hyperbola x^2-y^2=c^2dot Show that the locus of P is the ellipse (x^2)/(c^2)+(y^2)/((2a)^2)=1.