First slide

Parabola

Question

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

Moderate

A

$y^{2} = 4 (x + 5)$
B

$y^{2} = 4 (x + 4)$
C

$y^{2} = 4 (x + 3)$
D

$y^{2} = 4 (x - 3)$

Solution

We have $\sqrt{(x + 3)^{2} + y^{2}} = | x + 5 |$
$\Rightarrow y^{2} = (x + 5)^{2} - (x + 3)^{2} = 4 (x + 4)$ .

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