Conic Sections ...

The length of the latus rectum of the parabola $$4y^{2}+2x-20y+17=0$$ is:

The locus of the moving point $$P(x,y)$$ satisfying $$\sqrt { { \left( { x-1 } \right)  }^{ 2 }+{ y }^{ 2 } } +\sqrt { { \left( { x+1 } \right)  }^{ 2 }+({ y-{ \sqrt { 12 } ) }^{ 2 } } } =$$ a will be an ellipse if 

A circle has radius $$3$$ units and its centre lies on the line $$y=x-1$$. Then the equation of this circle if it passes through the point $$(7, 3)$$, is?

$$ABCD$$ is a square with side $$a$$. If $$AB$$ and $$AD$$ are taken as positive coordinate axes then equation of circle circumscribing the square is

For the ellipse $$ {12x}^{2} +{4y}^{2} +24x-16y+25=0 $$

The latus rectum of the conic $${ 3x }^{ 2 }+{ 4y }^{ 2 }-6x+8y-5=0$$ is ________________________.

The circle passing through $$\left(t,1\right),\left(1,t\right)$$ and $$\left(t,t\right)$$ for all values of $$t$$ also passes through 

The ratio of the ordinates of a point and its corresponding point is $$\frac { 2 \sqrt { 2 } } { 3 }$$ then eccentricity is ____________________.

Identify the types of cuves with represent by the equation $$\frac { { x }^{ 2 } }{ 1-r } -\frac { { y }^{ 2 } }{ 1+t } =1 $$, where $$r>1$$
is _______________.

The equation of the circle which passes through the point (3,-2) and (-2,0) and centre line 2x-y=3,is