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 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

The number of normals to the hyperbola (x^(2))/(a^(2))-(y^(2))/(b^(2))=1 from an external point, 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=

If the tangent at the point (asec alpha, b tanalpha ) to the hyberbola (x^(2))/(a^(2)) -(y^(2))/(b^(2)) =1 meets the transverse axis at T. Then the distances of T form a focus of the hyperbola is

Find the equations of the tangent and normal to the hyperbola (x^(2))/(a^(2))-(y^(2))/(b^(2))=1 at the point

Let P(4,3) be a point on the hyperbola (x^(2))/(a^(2))-(y^(2))/(b^(2))=1 . If the normal at P intersects the x-axis at (16,0), then the eccentricity of the hyperbola is