The equation of the normal to the hyperbola $\frac{x^2}{16} - \frac{y^2}{9} = 1$ at $(-4, 0)$ is

If the eccentricity of the hyperbola $\frac{x^2}{a^2}-\frac{y^2}{b^2}=1$ is $\sec \alpha$,then the area of the triangle formed by the asymptotes of the hyperbola with any of its tangent is

Let $P(x_0, y_0)$ be the point on the hyperbola $3x^2 - 4y^2 = 36$ which is nearest to the line $3x + 2y = 1$. Then $\sqrt{2}(y_0 - x_0)$ is equal to:

If the variable line $y = kx + 2h$ is tangent to an ellipse $2x^2 + 3y^2 = 6$,the locus of $P(h, k)$ is a conic $C$ whose eccentricity equals

Find the equation of the tangent to the hyperbola $\frac{x^2}{3} - \frac{y^2}{2} = 1$ which is equally inclined to the axes.

The angle between the asymptotes of the hyperbola $x^2-3y^2=3$ is