Question

Find the focus and the directrix of the parabola with the equation y = –1∕2 (x – 8)2 – 6.


A) Focus = (–8,–61∕2), directrix is y = –51∕2

B) Focus = (–8,–51∕2), directrix is y = –61∕2

C) Focus = (8,–61∕2), directrix is y = –51∕2

D) Focus = (8,–51∕2), directrix is y = –61∕2

Answer 1

Answer:

c

Step-by-step explanation:

Answer 2

The focus of the parabola is (–8,–51∕2), directrix is y = –61∕2 option (C) is correct.

What is a parabola?

It is defined as the graph of a quadratic function that has something bowl-shaped.

(x - h)² = 4a(y - k)

(h, k) is the vertex of the parabola:

a = √[(c-h)² + (d-k²]

(c, d) is the focus of the parabola:

We have an equation for the parabola:

The parabolic equation also in the form of quadratic equation.

Any equation of the form $\rm ax^2+bx+c=0$  where x is variable and a, b, and c are any real numbers where a ≠ 0 is called a quadratic equation.

y = (-1∕2)(x – 8)² – 6

The vertex of the parabola is (h, k)

h = 8, k = -6

The focus of the parabola:

(c, d)

c = -6

d = -6 - 1/2 = -13/2 = -6 1/2

Directrix of the parabola:

y = -6 - (-1/2)

y = -6 + 1/2

y = -11/2 = -5 1/2

Thus, the focus of the parabola is (–8,–51∕2), directrix is y = –61∕2 option (C) is correct.

Learn more about the parabola here:

brainly.com/question/8708520

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