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 the normal at a pont P to the hyperbola x^2/a^2 - y^2/b^2 =1 meets the x-axis at G , show that the SG = eSP.S being the focus of the hyperbola.

If the normal at any point P on the ellipse cuts the major and minor axes in G and g respectively and C be the centre of the ellipse, then

If the normal at P(asectheta,btantheta) to the hyperbola x^2/a^2-y^2/b^2=1 meets the transverse axis in G then minimum length of PG is

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).

P is a point on the hyperbola (x^2)/(a^2)-(y^2)/(b^2)=1,N is the foot of the perpendicular from P on the transverse axis. The tangent to the hyperbola at P meets the transvers axis at Tdot If O is the center of the hyperbola, then find the value of O TxO Ndot

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)

If the normal at any point P on the ellipse x^2/a^2+y^2/b^2=1 meets the axes at G and g respectively, then find the raio PG:Pg= (a) a : b (b) a^2 : b^2 (c) b : a (d) b^2 : a^2

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

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

N is the foot of the perpendicular from P on the transverse axis. The tangent to the hyperbola at P meets the transverse axis at T. If O is the center of the hyperbola the OT.ON is equal to: