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

(-2, 0)

Explanation:

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

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

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

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

Given equation:

`x=-\frac18y^2`

Rewrite in standard form:

`\implies (x-0)=-\frac18(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)`