Conic Sections ...

The length of the latus rectum of the parabola, $$y^2-6y+5x=0$$ is

The equation $${ x }^{ 2 }+{ y }^{ 2 }+4x+6y+13=0\quad $$ represents 

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

If $$  P S Q  $$ is the focal chord of the parabola $$  y^{2}=8 x  $$ such that $$  S P=6  $$ . Then the length of $$SQ$$ is

The equation of circle at center $$(3,4)$$ and radius $$5$$.

The curve for which the normal at any point (x,y) and the line joining origin to that point form and isosceles triangle with the x-axis as base is 

If C is the centre and A, B are two points on the conic $${ 4x }^{ 2 }+{ 9y }^{ 2 }-8x-36y+4=0$$ such that $$\angle ABC-\dfrac { \pi  }{ 2 } ,$$ then $$\begin{matrix} 1 & \quad \quad +\quad \quad \quad \quad \quad 1 \\ { CA }^{ 2 } & \quad \quad \quad \quad { CB }^{ 2 } \end{matrix}=$$

If two distinct chords of a parbola $${ y }^{ 2 }=4ax$$ passing through (a , 2a) are bisected on the line x + y =1, then the length of the latnsrectum can be 

If the parabola $${y^2} = 4\,\,ax$$ passes through the point $$\left( { - 3,2} \right),$$ then the length of its latus rectum is 

Match the column I with column II and mark the correct option from the codes given below.