Find the focus of the parabola $y = - 2 (x + 4)^{2} - 1$ .

(- 4, - 1)

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(- 4, \frac{9}{8})

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(- 4, 1)

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(- 4, - \frac{9}{8})

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Solution

The correct option is B $(- 4, - \frac{9}{8})$
Given, $y = - 2 {(x + 4)}^{2} - 1$
$\Rightarrow y + 1 = - 2 {(x + 4)}^{2} \Rightarrow {(x + 4)}^{2} = - \frac{1}{2} (y + 1) \Rightarrow 4 a = - \frac{1}{2}$
$\Rightarrow a = - \frac{1}{8}$
The focus of $x^{2} = 4 a y$ is $(0, a)$ .
Let $(h, k)$ be the focus of given parabola
$\Rightarrow h + 4 = 0, k + 1 = - \frac{1}{8} \Rightarrow x = - 4, y = - \frac{9}{8}$
So, the focus is $(- 4, - \frac{9}{8})$ .
Option D is correct.

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Find the focus of the parabola y=−2(x+4)2−1.

The correct option is B (−4,−98)Given, y=−2(x+4)2−1⇒y+1=−2(x+4)2⇒(x+4)2=−12(y+1)⇒4a=−12⇒a=−18The focus of x2=4ay is (0,a).Let (h,k) be the focus of given parabola⇒h+4=0,k+1=−18⇒x=−4,y=−98So, the focus is (−4,−98).Option D is correct.

Find the focus of the parabola $y = - 2 (x + 4)^{2} - 1$ .