Conic Sections ...

The latus rectum of parabola $${ y }^{ 2 }=5x+4y+1$$ is

A circle touch the line L and the circle $${ C }_{ 1 }$$ externally such that both the circles are on the same side of the line, then the locus of center of the circle is

If $$x ^ { 2 } + y ^ { 2 } - 2 x + 2 a y + a + 3 = 0$$ represents a real circle with non-zero radius, then most appropriate is?

Equation of the circle whose radius is 3 and centre is $$(-1,2)$$

If the equation $$p{ x }^{ 2 }+(2-q)xy+3{ y }^{ 2 }-6qx+30y+6q=0$$ represents a circle, then the values of p and q are

The length of the lotus rectum of the parabola $$9x^{2}-6x+36y+19=0$$

Equation of the circle whose radius is $$a+b$$ and centre $$(a, -b)$$

The foci of a hyperbola with the foci of the ellipse $$\frac { { x }^{ 2 } }{ 25 } +\frac { { y }^{ 2 } }{ 12 } =1.$$ Find the equation of the hyperbola, if its eccentricity is 2.

If $$  x^{2}+y^{2}-2 x+2 a y+a+3=0  $$ represents a real circle with non-zero radius, then most appropriate is

Find the equation of a circle whose cemtre is $$\left( {2,1} \right)$$ and radius is 3