Conic Sections Question 518
Question: The vertex of a parabola is the point, (a,b) and the latus rectum is of length, l. the axis of the parabola is parallel to the y-axis and the parabola is concave upward, then its equation is
Options:
A) $ {{(x+a)}^{2}}=\frac{1}{2}(2y-2b) $
B) $ {{(x-a)}^{2}}=\frac{1}{2}(2y-2b) $
C) $ {{(x+a)}^{2}}=\frac{1}{4}(2y-2b) $
D) $ {{(x-a)}^{2}}=\frac{1}{8}(2y-2b) $
Show Answer
Answer:
Correct Answer: A
Solution:
[a] The parabola having the axis parallel to the y-axis is $ {{(x-a)}^{2}}=4A(y-b) $ According to the question, the length of latus rectum is 4A=1.
Hence, the equation of the parabola is $ {{(x-a)}^{2}}=1(y-b) $ Or $ {{(x-a)}^{2}}=\frac{1}{2}(2y-2b) $
BETA
