Let $$P$$ $$\left( {a\,\sec \,\theta ,\,\,b\,\tan \theta } \right)$$ and $$Q$$ $$\left( {a\,\sec \,\,\phi ,\,\,b\,\tan \,\phi } \right)$$, where $$\theta + \phi = \pi /2,$$, be two points on the hyperbola $${{{x^2}} \over {{a^2}}} - {{{y^2}} \over {{b^2}}} = 1$$.

If $$(h, k)$$ is the point of intersection of the normals at $$P$$ and $$Q$$, then $$k$$ is equal to

The curve described parametrically by $$x = {t^2} + t + 1,$$ $$y = {t^2} - t + 1 $$ represents

If $$x$$ $$=$$ $$9$$ is the chord of contact of the hyperbola $${x^2} - {y^2} = 9,$$ then the equation of the vcorresponding pair of tangents is

The number of values of $$c$$ such that the straight line $$y=4x + c$$ touches the curve $$\left( {{x^2}/4} \right) + {y^2} = 1$$ is