Questions in conic-section

Select	Question
	The locus of the point of intersection of lines $(x+y)t=a$ and $x-y=at$, where t is the parameter, is
	The equation of the hyperbola referred to its axes as axes of coordinate and whose distance between the foci is 16 and eccentricity is $\sqrt{2}$, is
	If the foci of the ellipse $\frac{{{x}^{2}}}{16}+\frac{{{y}^{2}}}{{{b}^{2}}}=1$ and the hyperbola $\frac{{{x}^{2}}}{144}-\frac{{{y}^{2}}}{81}=\frac{1}{25}$ coincide, then the value of ${{b}^{2}}$ is
	A tangent to a hyperbola $\frac{{{x}^{2}}}{{{a}^{2}}}-\frac{{{y}^{2}}}{{{b}^{2}}}=1$ intercepts a length of unity from each of the co-ordinate axes, then the point (a, b) lies on the rectangular hyperbola
	Curve $xy={{c}^{2}}$ is said to be
	The reciprocal of the eccentricity of rectangular hyperbola, is
	The eccentricity of the hyperbola $\frac{\sqrt{1999}}{3}({{x}^{2}}-{{y}^{2}})=1$ is
	If transverse and conjugate axes of a hyperbola are equal, then its eccentricity is
	If $5{{x}^{2}}+\lambda {{y}^{2}}=20$ represents a rectangular hyperbola, then $\lambda $ equals
	The equation of the hyperbola referred to the axis as axes of co-ordinate and whose distance between the foci is 16 and eccentricity is $\sqrt{2}$, is