`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`

Ifthe normal at P to the rectangular hyperbola x^2-y^2=4 meets the axes in G and g and C is the centre of the hyperbola, then

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).

The slope of the tangent to the rectangular hyperbola xy=c^(2) at the point (ct,(c)/(t)) is -

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

Determine the area bounded by rectangular hyperbola xy=c^2 the x-axis and the two ordinated x=c,x=2c.

In a rectangular hyperbola x^2-y^2=a^2 , prove that SP.S'P=CP^2 , where C is the centre and S, S' are the foci and P is any point on the hyperbola.

If S, S' are the foci and' P any point on the rectangular hyperbola x^2 - y^2 =a^2 , prove that, bar(SP).bar(S'P) = CP^2 where C is the centre of the hyperbola

Find the coordinates of points on the hyperbola xy=c^(2) at which the normal is perpendicular to the line x+t^(2)y=2c

If tangents O Q and O R are dawn to variable circles having radius r and the center lying on the rectangular hyperbola x y=1 , then the locus of the circumcenter of triangle O Q R is (O being the origin). (a) x y=4 (b) x y=1/4 x y=1 (d) none of these