JEE Main 2007 — Coordinate Geometry

The equation of a tangent to the parabola $y^2=8 x$ is $y=x+2$. The point on this line from which the other tangent to the parabola is perpendicular to the given tangent is

Let $A(h, k), B(1,1)$ and $C(2,1)$ be the vertices of a right angled triangle with $A C$ as its hypotenuse. If the area of the triangle is $1$, then the set of values which ' $\mathrm{k}$ ' can take is given by

For the hyperbola $\frac{x^2}{\cos ^2 \alpha}-\frac{y^2}{\sin ^2 \alpha}=1$, which of the following remains constant when $\alpha$ varies?