Conic Sections ...

If the radius of the circle $$ x ^ { 2 } + y ^ { 2 } $$ - 18 x - 12 y + k = 0 be 11 then k =

The equations $$x=\frac{t}{4},y=\frac{t^2}{4}$$ represents

The latus rectum of a parabola whose focal chord is PSQ such that SP=3 and SQ=2 is given by

If $$\frac { (3x-4y-{ 1) }^{ 2 } }{ 100 } -\frac { (4x+3y-{ 1) }^{ 2 } }{ 225 } =1,$$ then
length latusrectum of hyperbola is-

If  $$y ^ { 2 } - 2 x - 2 y + 5 = 0$$  is

The equation $$\dfrac{x^2}{10 - a} + \dfrac{y^2}{4 - a} = 1$$ , represents an ellipse , if 

The equation of circle with centre (1, 2) and tangent $$x + y - 5 = 0$$ is

The distance between the foci or a hyperbola is double the distance between its vertices and the length of a conjugate axis is 6. The equation of the hyperbola referred to its axes as axes of coordinates is

The equation of directrix of a parabola is 3x + 4y + 15 =0 and equation of tangent at vertex is 3x + 4y - 5= 0. Then the length of latus recturn is equal to 

Length of the latus rectum of the parabola $$25\left[ { \left( x-2 \right)  }^{ 2 }+{ \left( y-3 \right)  }^{ 2 } \right] ={ \left( 3x-4y+7 \right)  }^{ 2 }$$ is