Question

If \[ P\equiv y^2+2y-x+6=0 \] is a parabola. \(S=0\) is another parabola such that the axes of \(S=0\) and \(P=0\) are same and the distance between their foci is \[ \frac54. \] If the foci of these parabolas are on either side of the vertex of \(S=0\) and the vertex of \(S=0\) is on the directrix of \(P=0\), then the length of latus rectum of \(S=0\) is

• A. \(1\)
• B. \(3\)
• C. \(\dfrac{18}{4}\)
• D. \(4\)

Hint:

For the parabola \[ (y-k)^2=4a(x-h), \] remember: \[ \boxed{\text{Focus }=(h+a,k),\qquad \text{Directrix }x=h-a,\qquad \text{Latus rectum}=4a.} \]

Answer 1

The Correct Option is B