Question

A parabola has x- axis as its axis, y- axis as its directrix and $4a$ as its latus rectum. If the focus lies to the left side of the directrix then the equation of the parabola is

• A. $y^2=4a(x+a)$
• B. $y^2=4a(x-a)$
• C. $y^2=-4a(x+a)$
• D. $y^2=4a(x-2a)$

Answer 1

Answer: (C)

$y^2=-4a(x+a)$

Let $P(x,y)$ be a point on the parabola
Given that the directrix is y-axis
So, coordinates of any point $M$ on directrix is of the form $(0,y)$
Length of latus rectum $=4a=2\left(2a\right)$
Since, axis of parabola is x-axis, and focus is on left side of directrix
So, focus is at $(-2a,0)$
By definition of parabola,
$PS=PM$
$(x+2a{)}^2+y^2=x^2$
$\Rightarrow y^2=-4ax-4a^2$
$\Rightarrow y^2=-4a(x+a)$