Mathematics: If given the equation x = -1/8(y + 6)^2 + 2 what is the location of the focus point

30Step-by-step explanation:7+23 =30...

If given the equation x = -1/8(y + 6)^2 + 2 what - id186223546730, buddyclayjohnson

yoyoyo42

08.01.2022

Focus is at (0,-6) .

Step-by-step explanation:

Given:

The equation of the parabola is: $x=-\frac{1}{8}(y+6)^{2}+2$

The standard form of a parabola in vertex form is given as:

$(y-k)^{2}=4p(x-h)$

Where, (h,k) is the vertex of parabola. The value of decides the nature of parabola.

If p 0 , the parabola opens rightwards and if , the parabola opens leftwards.

Let us first rewrite the given equation in standard form.

$x=-\frac{1}{8}(y+6)^{2}+2\\x-2=-\frac{1}{8}(y+6)^{2}\\-8(x-2)=(y+6)^{2}\\(y-(-6))^{2}=4(-2)(x-2)$

On comparing the above equation with the standard one, we get,

h=2,k=-6,p=-2

Therefore, the focus of a parabola of the form $(y-k)^{2}=4p(x-h)$ is given by the point (h+p,k) .

∴ Focus is (h+p,k)=(2-2,-6)=(0,-6)

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