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Normal are drawn to the hyperbola (x^2)/...

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.

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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.

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If any line perpendicular to the transverse axis cuts the hyperbola (x^2)/(a^2)-(y^2)/(b^2)=1 and the conjugate hyperbola (x^2)/(a^2)-(y^2)/(b^2)=-1 at points Pa n dQ , respectively, then prove that normal at Pa n dQ meet on the x-axis.

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