Questions in conic-section

Select	Question
	The eccentricity of the hyperbola $5{{x}^{2}}-4{{y}^{2}}+20x+8y=4$ is
	The latus rectum of the hyperbola $9{{x}^{2}}-16{{y}^{2}}+72x-32y-16=0$ is
	The point of contact of the tangent $y=x+2$ to the hyperbola $5{{x}^{2}}-9{{y}^{2}}=45$ is
	The line $lx+my+n=0$ will be a tangent to the hyperbola $\frac{{{x}^{2}}}{{{a}^{2}}}-\frac{{{y}^{2}}}{{{b}^{2}}}=1$, if
	If the line $y=2x+\lambda $ be a tangent to the hyperbola $36{{x}^{2}}-25{{y}^{2}}=3600$, then $\lambda =$
	The line $3x-4y=5$is a tangent to the hyperbola ${{x}^{2}}-4{{y}^{2}}=5$. The point of contact is
	The equation of the tangent at the point $(a\sec \theta ,\ b\tan \theta )$ of the conic $\frac{{{x}^{2}}}{{{a}^{2}}}-\frac{{{y}^{2}}}{{{b}^{2}}}=1$, is
	The equation of the tangents to the conic $3{{x}^{2}}-{{y}^{2}}=3$ perpendicular to the line $x+3y=2$ is
	The equation of the tangent to the hyperbola $2{{x}^{2}}-3{{y}^{2}}=6$which is parallel to the line $y=3x+4$, is
	The locus of the point of intersection of any two perpendicular tangents to the hyperbola is a circle which is called the director circle of the hyperbola, then the eqn of this circle is