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icang [17]
3 years ago
11

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

Mathematics
1 answer:
HACTEHA [7]3 years ago
4 0

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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