First slide

Parabola

Question

The vertex of a parabola is the point (a, b) and the latus rectum is of length $l$ . If the axis of the parabola is parallel to the $y -$ axis and the parabola is concave upward, then its equation is

Moderate

A

$(x + a)^{2} = \frac{l}{2} (2 y - 2 b)$
B

$(x - a)^{2} = \frac{l}{2} (2 y - 2 b)$
C

$(x + a)^{2} = \frac{l}{4} (2 y - 2 b)$
D

$(x - a)^{2} = \frac{l}{8} (2 y - 2 b)$

Solution

The parabola having the axis parallel to the y-axis is
$(x - a)^{2} = 4 A (y - b)$
According to the question, the length of latus rectum is 4A = $l$ .
Hence, the equation of the parabola is
$\begin{array}{l} (x - a)^{2} = l (y - b) \\ or (x - a)^{2} = \frac{l}{2} (2 y - 2 b) \end{array}$

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