The normla to the hyperbola `(x^2)/(a^2)-(y^2)/(b^2)=1` drawn at an extremity of its latus rectum is parallel to an asymptote. Show that the eccentricity is equal to the square root of `(1+sqrt(5))//2.`

If normal to hyperbola x^2/a^2-y^2/b^2=1 drawn at an extremity of its latus-rectum has slope equal to the slope of line which meets hyperbola only once, then the eccentricity of hyperbola is

If normal to hyperbola (x^(2))/(a^(2))-(y^(2))/(b^(2))=1 drawn at an extremity of its latus-rectum has slope equal to the slope of line which meets hyperbola only once,then the eccentricity of hyperbola is

If normal to hyperbola x^2/a^2-y^2/b^2=1 drawn at an extremity of its latus-rectum has slope equal to the slope of line which meets hyperbola only once, then the eccentricity of hyperbola is

The normal drawn to the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1 at the extremity of the latus rectum passes through the extremity of the minor axis.Eccentricity of this ellipse is equal

The eccentricity of the hyperbola x^2/a^2-y^2/b^2=1 if the length of its latus rectum is equal to length of its semi conjugate axis, is:

The latus rectum of the hyperbola x^2/9-y^2/16=1 is _____.

If e is the eccentricity of the hyperbola (x^(2))/(a^(2))-(y^(2))/(b^(2))=1 and theta is the angle between the asymptotes, then cos.(theta)/(2) is equal to

If e is the eccentricity of the hyperbola (x^(2))/(a^(2))-(y^(2))/(b^(2))=1 and theta is the angle between the asymptotes, then cos.(theta)/(2) is equal to

If e is the eccentricity of the hyperbola (x^(2))/(a^(2))-(y^(2))/(b^(2))=1 and theta is the angle between the asymptotes, then cos.(theta)/(2) is equal to