The tangent at the point P of a rectangular hyperbola meets the asymptotes at L and M and C is the centre of the hyperbola. Prove that `PL=PM=PC`.

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 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

The normal at three points P, Q, R on a rectangular hyperbola intersect at a point T on the curve. Prove that the centre of the hyperbola is the centroid of the triangle PQR.

Prove that the eccentricity of a rectangular hyperbola is equal to sqrt2 .

The differential equation of the rectangular hyperbola whose axes are the asymptotes of the hyperbola, is

The coordinates of a point on the rectangular hyperbola xy=c^2 normal at which passes through the centre of the hyperbola are

If the normal to the rectangular hyperbola x^(2) - y^(2) = 4 at a point P meets the coordinates axes in Q and R and O is the centre of the hyperbola , then

Normal at 3 points P, Q, and R on a rectangular hyperbola intersect at a point on a curve the centroid of triangle PQR

If the normal at a point P to the hyperbola meets the transverse axis at G, and the value of SG/SP is 6, then the eccentricity of the hyperbola is (where S is focus of the hyperbola)

C is the center of the hyperbola (x^2)/(a^2)-(y^2)/(b^2)=1 The tangent at any point P on this hyperbola meet the straight lines b x-a y=0 and b x+a y=0 at points Qa n dR , respectively. Then prove that C QdotC R=a^2+b^2dot