The focal distance of the point `(a sec theta,b tan theta)` from the focus `S(ae,0)` in the hyperbola `(x^(2))/(a^(2))-(y^(2))/(b^(2))=1` is

If the chord joining the points (a sec theta_(1),b tan theta_(1)) and (a sec theta_(2),b tan theta_(2)) on the hyperbola (x^(2))/(a^(2))-(y^(2))/(b^(2))=1 is a focal chord,then prove that tan((theta_(1))/(2))tan((theta_(2))/(2))+(ke-1)/(ke+1)=0, where k=+-1

If x=a sec theta,y=b tan theta, then prove that (x^(2))/(a^(2))-(y^(2))/(b^(2))=1

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

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 P(a sec alpha,b tan alpha) and Q(a secbeta, b tan beta) are two points on the hyperbola (x^(2))/(a^(2))-(y^(2))/(b^(2))=1 such that alpha-beta=2theta (a constant), then PQ touches the hyperbola

Let P(a sec theta,b tan theta) and Q(a sec c phi,b tan phi) (where theta+phi=(pi)/(2) be two points on the hyperbola (x^(2))/(a^(2))-(y^(2))/(b^(2))=1 If (h,k) is the point of intersection of the normals at P and Q then k is equal to (A) (a^(2)+b^(2))/(a)(B)-((a^(2)+b^(2))/(a))( C) (a^(2)+b^(2))/(b)(D)-((a^(2)+b^(2))/(b))

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

If the tangent at the point (2sec theta,3tan theta) of the hyperbola (x^(2))/(4)-(y^(2))/(9)=1 then the value of theta

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