Conic Sections ...

Eccentricity of the hyperbola $$x^{2}-y^{2}=4$$ is 

A circle has its centre on the $$y-axis$$ and passes through the origin, touches another circle with centre $$(2,2)$$ and radius 2, then the radius of the circle is 

$$L L ^ { '}$$ is the latus rectum of an ellipse and $$\triangle S ^ { \prime } L L ^ { ' }$$ is an equilateral triangle. Then $$e =$$

Length of the latus rectum of the parabola $$\sqrt {x}+\sqrt {y}=\sqrt {a}$$ is

If there is exactly one tangent at a distance of $$4$$ units from one of the focus of $$\dfrac {x^{2}}{a^{2}}+\dfrac {y^{2}}{a^{2}-16}=1,a > 4$$, the length of latus rectum is :-

Distance between the foci of the curve represented by the equation $$x=3+4\cos\theta, y=2+3\sin\theta$$, is?

The equation $$\dfrac{x^2}{2-r}+\dfrac{y^2}{r-5}+1=0$$ represents an ellipse, if

A variable circle is drawn to touch the x-axis at the origin.The locus of the pole at the straight line $$6 x + m y + n = 0$$ w.r.t. the variable circle has the equation:-

General solution of the equation $$ y=x\dfrac{dy}{dx}+\dfrac {dx}{dy}$$ represents _____________.

Equation of circles which touch both the axes and whose centres are at a distance of $$2\sqrt {2}$$ units from origin are