Conic Sections Question 8
Question: The vertex of a parabola is the point (a, b) and latus rectum is of length l. If the axis of the parabola is along the positive direction of y-axis, then its equation is
Options:
A) $ {{(x+a)}^{2}}=\frac{l}{2}(2y-2b) $
B) $ {{(x-a)}^{2}}=\frac{l}{2}(2y-2b) $
C) $ {{(x+a)}^{2}}=\frac{l}{4}(2y-2b) $
D) $ {{(x-a)}^{2}}=\frac{l}{8}(2y-2b) $
Show Answer
Answer:
Correct Answer: B
Solution:
The equation of the parabola referred to its vertex as the origin is $ X^{2}=lY, $ where $ x=X+a,y=Y+b $ . Therefore the equation of the parabola referred to the point (a,b) as the vertex is $ {{(x-a)}^{2}}=l(y-b) $ or $ {{(x-a)}^{2}}=\frac{l}{2}(2y-2b) $ .
BETA
