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 normals at P(theta) and Q((pi)/(2)+theta) to the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1 meet the major axis at G and g, respectively,then PG^(2)+Qg^(2)=b^(2)(1-e^(2))(2-e)^(2)a^(2)(e^(4)-e^(2)+2)a^(2)(1+e^(2))(2+e^(2))b^(2)(1+e^(2))(2+e^(2))

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.

The distance of the point 'theta' on the ellipse x^(2)/a^(2) + y^(2)/b^(2) = 1 from a focus, is

The distance of the point theta on the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1 from a focus is

Length of the focal chord of the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1 which is inclined to the major axis at angle theta is

Find the focal distance of point P(theta) on the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1

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 length of the major axis intercepted between the tangent and normal at a point P (a cos theta, b sin theta) on the ellipse (x^(2))/(a^(2)) +(y^(2))/(b^(2)) =1 is equal to the length of semi-major axis, then eccentricity of the ellipse is

If the circle whose diameter is the major axis of the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1(a gt b gt 0) meets the minor axis at point P and the orthocentre of DeltaPF_(1)F_(2) lies on the ellipse, where F_(1) and F_(2) are foci of the ellipse, then the square of the eccentricity of the ellipse is