Question

x= -1/8y2
The focus of the parabola is:
O (0, -2)
O (2, 0)
O (-2, 0)

Answer 1

x=-1/8y²

Interchange x and y

• y=-1/8x²

Compare to Vertex form y=a(x-h)²+k

• a=-1/8

Now

• 1/4a
• 1/4(-1/8)
• -2

.So

Focus (-2,0)

Answer 2

Answer:

(-2, 0)

Step-by-step explanation:

Standard form of a parabola with a horizontal axis of symmetry:

$(y-k)^2=4p(x-h)\quad \textsf{where}\:p\neq 0$

$\textsf{Vertex}=(h, k)$

$\textsf{Focus}=(h+p,k)$

Given equation:

$x=-\dfrac18y^2$

Rewrite in standard form:

$\implies (x-0)=-\dfrac18(y-0)^2$

$\implies -8(x-0)=(y-0)^2$

$\implies (y-0)^2=-8(x-0)$

Comparing with the general standard form:

• k = 0
• h = 0
• 4p = -8 ⇒ p = -2

Therefore:

$\textsf{Vertex }(h,k)=(0,0)$

$\textsf{Focus }(h+p,k)=(0-2,0)=(-2,0)$