Conic Sections ...

The equation of the circle whose centre and radius are $$\left( 1,-1 \right) $$ and $$4$$ respectively, is

For hyperbola $$\dfrac{x^2}{cos^2a}-\dfrac{y^2}{sin^2a}=1$$ which of the following remains constant with change in 'a'?

The distance between the foci of the hyperbola $${ x }^{ 2 }-3{ y }^{ 2 }-4x-6y-11=0$$ is

The equation of the ellipse having vertices at $$\displaystyle \left( \pm 5,0 \right) $$ and foci $$\displaystyle \left( \pm 4,0 \right) $$ is

The equation of a parabola which passes through the intersection of a straight line x$$+$$y$$=0$$ and the circle $$x^2+y^2+4y=0$$ is.

The equation to the circle with centre $$(2, 1)$$ and touching the line $$3x + 4y = 5$$ is

Find the equation of a circle with center $$(2,0)$$ and passing through point $$\left( 3,\sqrt { 3 }  \right) $$. 

The radius of the circle $$x^{2} + y^{2} + 4x + 6y + 13 = 0$$ is

The sum of the focal distances of any point on the conic $$\dfrac {x^{2}}{25} + \dfrac {y^{2}}{16} = 1$$ is