Questions in conic-section

Select	Question
	The line $y=mx+c$ touches the curve $\frac{{{x}^{2}}}{{{a}^{2}}}-\frac{{{y}^{2}}}{{{b}^{2}}}=1$, if
	The straight line $x+y=\sqrt{2}p$will touch the hyperbola $4{{x}^{2}}-9{{y}^{2}}=36$, if
	The equation of the director circle of the hyperbola $\frac{{{x}^{2}}}{16}-\frac{{{y}^{2}}}{4}=1$ is given by
	The equation of the tangent parallel to $y-x+5=0$ drawn to $\frac{{{x}^{2}}}{3}-\frac{{{y}^{2}}}{2}=1$ is
	Let E be the ellipse $\frac{{{x}^{2}}}{9}+\frac{{{y}^{2}}}{4}=1$ and C be the circle ${{x}^{2}}+{{y}^{2}}=9$. Let P and Q be the points (1, 2) and (2, 1) respectively. Then
	The length of the chord of the parabola ${{y}^{2}}=4ax$ which passes through the vertex and makes an angle $\theta $ with the axis of the parabola, is
	The equation of the normal at the point $(a\sec \theta ,\ b\tan \theta )$ of the curve ${{b}^{2}}{{x}^{2}}-{{a}^{2}}{{y}^{2}}={{a}^{2}}{{b}^{2}}$ is
	The condition that the straight line $lx+my=n$ may be a normal to the hyperbola ${{b}^{2}}{{x}^{2}}-{{a}^{2}}{{y}^{2}}={{a}^{2}}{{b}^{2}}$ is given by
	The equation of the normal to the hyperbola $\frac{{{x}^{2}}}{16}-\frac{{{y}^{2}}}{9}=1$ at the point $(8,\ 3\sqrt{3})$ is
	The equation of the normal at the point (6, 4) on the hyperbola $\frac{{{x}^{2}}}{9}-\frac{{{y}^{2}}}{16}=3$, is