Question

The equation of the parabola whose vertex is $(-3,0)$ and directrix is $x+5=0,$ is

• A. $x^2=8(y+3)$
• B. $y^2=8(x+3)$
• C. $x^2=8(y-3)$
• D. $y^2=8(x-3)$

Answer 1

The correct option is B $y^2=8(x+3)$


A line passing through the vertex $(-3,0)$ and perpendicular to directrix $x+5=0$ is the axis of the parabola by definition which is $x-$axis.
Let focus of the parabola be $(a,0).$
Since vertex is the middle point of $(-5,0)$ and focus $F(a,0),$
$\therefore -3=\frac{(a-5)}{2}\Rightarrow a=-1\therefore \text{Focus}=(-1,0)$
Thus, the equation the parabola is
$(x+1{)}^2+y^2=(x+5{)}^2\Rightarrow y^2=8(x+3)$