`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`

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

Normal to a rectangular hyperbola at P meets the transverse axis at N. If foci of hyperbola are S and S', then find the value of (SN)/(SP).

At the point of intersection of the rectangular hyperbola xy=c^2 and the parabola y^2=4ax tangents to the rectangular hyperbola and the parabola make angles theta and phi , respectively with x-axis, then

The length of the transverse axis of the rectangular hyperbola x y=18 is 6 (b) 12 (c) 18 (d) 9

If the normal at P to the rectangular hyperbola x^2-y^2=4 meets the axes at G and ga n dC is the center of the hyperbola, then (a) P G=P C (b) Pg=P C (c) P G-Pg (d) Gg=2P C

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

If P(x_1,y_1),Q(x_2,y_2),R(x_3,y_3) and S(x_4,y_4) are four concyclic points on the rectangular hyperbola and xy = c^2 , then coordinates of the orthocentre ofthe triangle PQR 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.

The chord P Q of the rectangular hyperbola x y=a^2 meets the axis of x at A ; C is the midpoint of P Q ; and O is the origin. Then A C O is equilateral (b) isosceles right-angled (d) right isosceles

Let 'p' be the perpendicular distance from the centre C of the hyperbola x^2/a^2-y^2/b^2=1 to the tangent drawn at a point R on the hyperbola. If S & S' are the two foci of the hyperbola, then show that (RS + RS')^2 = 4 a^2(1+b^2/p^2) .