If the normal at `P(theta)` on the hyperbola `(x^2)/(a^2)-(y^2)/(2a^2)=1` meets the transvers axis at `G ,` then prove that `A GdotA^(prime)G=a^2(e^4sec^2theta-1)` , where `Aa n dA '` are the vertices of the hyperbola.

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

If the normal at 'theta' on the hyperbola (x^(2))/(a^(2))-(y^(2))/(b^(2))=1 meets the transverse axis at G , and A and A' are the vertices of the hyperbola , then AC.A'G= (a) a^2(e^4 sec^2 theta-1) (b) a^2(e^4 tan^2 theta-1) (c) b^2(e^4 sec^2 theta-1) (d) b^2(e^4 sec^2 theta+1)

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.

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

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 T×O Ndot

If the eccentricity of the hyperbola conjugate to the hyperbola (x^2)/(4)-(y^2)/(12)=1 is e, then 3e^2 is equal to:

If the normal at point P (theta) on the ellipse x^2/a^2 + y^2/b^2 = 1 meets the axes of x and y at M and N respectively, show that PM : PN = b^2 : a^2 .

P N is the ordinate of any point P on the hyperbola (x^2)/(a^2)-(y^2)/(b^2)=1 and AA ' is its transvers axis. If Q divides A P in the ratio a^2: b^2, then prove that N Q is perpendicular to A^(prime)Pdot

P N is the ordinate of any point P on the hyperbola (x^2)/(a^2)-(y^2)/(b^2)=1 and AA ' is its transvers axis. If Q divides A P in the ratio a^2: b^2, then prove that N Q is perpendicular to A^(prime)Pdot

P N is the ordinate of any point P on the hyperbola (x^2)/(a^2)-(y^2)/(b^2)=1 and AA ' is its transvers axis. If Q divides A P in the ratio a^2: b^2, then prove that N Q is