Amit M Agarwal Solutions for Chapter: Hyperbola, Exercise 2: Work Book Exercise 16.2

The equation of a tangent to the hyperbola $16x^2-25y^2-96x+100y-356=0$, which makes an angle $\frac{\pi }{4}$ with the transverse axis, is

The point of intersection of two tangents to the hyperbola $\frac{x^2}{a^2}-\frac{y^2}{b^2}=1$, the product of whose slopes is $c^2$, lies on the curve

The locus of the middle points of the portions of the tangents to the hyperbola $\frac{x^2}{a^2}-\frac{y^2}{b^2}=1$ intercepted between the coordinate axes, is

If radii of director circle of $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$ and $\frac{x^2}{a^2}-\frac{y^2}{b^2}=1$ are $2r$ and $r$ respectively and $e_e$ and $e_h$ are the eccentricities of the ellipse and hyperbola respectively, then