ParabolaHard
Question
Let P (x1, y1) and Q (x2, y2), y1 < 0, y2 < 0, be the end points of the latus rectum of the ellipse x2 + 4y2 = 4. The equations of parabolas with latus rectum PQ are
Options
A.x2 + 2√3 y = 3 + √3
B.x2 - 2√3 y = 3 + √3
C.x2 + 2√3 y = 3 - √3
D.x2 - 2√3 y = 3 - √3
Solution
b2 = a2 (1 - e2)
⇒ e =
⇒
and 
(given y1 and y2 less than 0). Co-ordinates of mid-point of PQ are
R ≡
PQ = 2√3 = length of latus rectum.
⇒ two parabola are possible whose vertices are
and 
Hence the equations of the parabolas are x2 - 2√3y = 3 + √3
and x2 + 2√3y = 3 - √3.
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