Normal are drawn to the hyperbola `(x^2)/(a^2)-(y^2)/(b^2)=1` at point `theta_1a n dtheta_2` meeting the conjugate axis at `G_1a n dG_2,` respectively. If `theta_1+theta_2=pi/2,` prove that `C G_1dotC G_2=(a^2e^4)/(e^2-1)` , where `C` is the center of the hyperbola and `e` is the eccentricity.

Normal are drawn to the hyperbola (x^2)/(a^2)-(y^2)/(b^2)=1 at point theta_1 and theta_2 meeting the conjugate axis at G_1a n dG_2, respectively. If theta_1+theta_2=pi/2, prove that C G_1*C G_2=(a^2e^4)/(e^2-1) , where C is the center of the hyperbola and e is the eccentricity.

Normal are drawn to the hyperbola (x^2)/(a^2)-(y^2)/(b^2)=1 at point theta_1 and theta_2 meeting the conjugate axis at G_1a n dG_2, respectively. If theta_1+theta_2=pi/2, prove that C G_1*C G_2=(a^2e^4)/(e^2-1) , where C is the center of the hyperbola and e is the eccentricity.

Normal are drawn to the hyperbola (x^(2))/(a^(2))-(y^(2))/(b^(2))=1 at point theta_(1) and theta_(2) meeting the conjugate axis at G_(1) and G_(2), respectively.If theta_(1)+theta_(2)=(pi)/(2), prove that CG_(1).CG_(2)=(a^(2)e^(4))/(e^(2)-1) where C is the center of the hyperbola and e is the eccentricity.

If the normal at theta on the hyperbola x^(2)//a^(2)-y^(2)//b^(2)=1 meets the transverse axis at G, then AG. A'G=

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=

If the normal at theta on the hyperbola x^(2)//a^(2) -y^(2) //b^(2) =1 meets the transverse axis at G , then AG . A'G =

If e is the eccentricity of the hyperbola (x^(2))/(a^(2))-(y^(2))/(b^(2))=1 and theta is the angle between the asymptotes, then cos.(theta)/(2) is equal to

If e is the eccentricity of the hyperbola (x^(2))/(a^(2))-(y^(2))/(b^(2))=1 and theta is the angle between the asymptotes, then cos.(theta)/(2) is equal to

If e is the eccentricity of the hyperbola (x^(2))/(a^(2))-(y^(2))/(b^(2))=1 and theta is the angle between the asymptotes, then cos.(theta)/(2) is equal to