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 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 P(a sec theta,b tan theta) 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 P(theta) on the hyperbola (x^(2))/(a^(2))-(y^(2))/(2a^(2))=1 meets the transvers axis at G, then prove that AG*A'G=a^(2)(e^(4)sec^(2)theta-1) where A and A' are the vertices of the hyperbola.

If the tangents at the point (a sec alpha, b tan alpha) to the hyperbola (x^(2))/(a^(2))-(y^(2))/(b^(2))=1 meets the transverse axis at T , then the distance of T from a focus of the hyperbola, is

If the normal at theta on the hyperola x^(2)/a^(2)-y^(2)/b^(2)=1 meets the transverse axis at G, prove that AG, A'G=a^(2) (e^(4) sec^(2) theta-1) . Where A and A' 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 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 P(theta) on the ellipse x^(2)/a^(2)+y^(2)/b^(2)=1 with focus S ,meets the major axis in G. then SG=