Question

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

• A. $y^2=4\left(x-4\right)$
• B. $y^2=2\left(x+4\right)$
• C. $y^2=4\left(x-3\right)$
• D. $y^2=4\left(x+4\right)$

Answer 1

The correct option is D $y^2=4\left(x+4\right)$

According to definition of parabola , is is the locks of the points in that planes that are equidistant from both focus and directrix.

Given, focus : (-3,0)

directrix : x + 5 = 0

Let (x ,y) is the point on the parabola .

∴ distance of point from focus = distance of point from directrix

⇒ $\sqrt{(x+3{)}^2+y^2}=|x+5|/\sqrt{(1^2+0^2)}$

⇒ $\sqrt{(x+3{)}^2+y^2}=|x+5|$

squaring both sides,

(x + 3)² + y² = (x + 5)²

⇒y² = (x + 5)² - (x + 3)²

⇒y² = (x + 5 - x - 3)(x + 5 + x + 3)

⇒y² = 2(2x + 8) = 4(x + 4)

Hence, equation of parabola is y² = 4(x + 4)