Questions in conic-section

Select	Question
	If e and e’ are the eccentricities of the ellipse $5{{x}^{2}}+9{{y}^{2}}=45$ and the hyperbola $5{{x}^{2}}-4{{y}^{2}}=45$ respectively, then $ee'=$
	The distance between the directrices of a rectangular hyperbola is 10 units, then distance between its foci is
	Eccentricity of the curve ${{x}^{2}}-{{y}^{2}}={{a}^{2}}$ is
	Eccentricity of rectangular hyperbola is
	The eccentricity of the hyperbola conjugate to ${{x}^{2}}-3{{y}^{2}}=2x+8$ is
	The locus of a point $P(\alpha ,\,\beta )$ moving under the condition that the line $y=\alpha x+\beta $ is a tangent to the hyperbola $\frac{{{x}^{2}}}{{{a}^{2}}}-\frac{{{y}^{2}}}{{{b}^{2}}}=1$ is
	The eccentricity of the hyperbola $\frac{{{x}^{2}}}{16}-\frac{{{y}^{2}}}{25}=1$ is
	The equation to the hyperbola having its eccentricity 2 and the distance between its foci is 8
	If $\theta$ is the acute angle of intersection at a real point of intersection of the circle ${{x}^{2}}+{{y}^{2}}=5$ and the parabola ${{y}^{2}}=4x$ then $\tan \theta$ is equal to
	The equation of the hyperbola in the standard form (with transverse axis along the x-axis) having the length of the latus rectum = 9 units and eccentricity = 5/4 is