2 years ago

Find The Area Of The Figure

Mathematics

1 answer:

vivado [14]2 years ago

6 0

Answer:

I'm not sure about that one sorry but I will look it up

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A parabola has a focus of F(8.5,−4) and a directrix of x=9.5.

HACTEHA [7]

Answer:

$-\frac{1}{2}y^2-4y+1=x$

Step-by-step explanation:

A parabola has a focus of F(8.5,−4) and a directrix of x=9.5.

General form of horizontal parabola is

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

the distance between directrix and focus is the value of p

so p = 8.5 - 9.5 = -0.5

Focus is (h+p , k), given focus is (8.5, -4)

So k = -4 and h+p = 8.5

we know p = -0.5

h +p = 8.5

h - 0.5 = 8.5

so h= 9 and k = -4

vertex is (h,k) that is (9, -4)

Now plug in the value in the general equation

$(y-k)^2=4p(x-h)$ , k= -4, h= 9 , p = -0.5

$(y+4)^2=4(-0.5)(x-9)$

$(y+4)^2=-2(x-9)$

$y^2+8y+16=-2x+18$

subtract 18 on both sides

$y^2+8y-2=-2x$

Divide whole equation by -2

$-\frac{1}{2}y^2-4y+1=x$

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