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igor_vitrenko [27]
3 years ago
14

Which equation represents a parabola that has a focus of (0 0) and a directrix of y = 2

Mathematics
2 answers:
Rainbow [258]3 years ago
4 0

Answer:

4. x^2 = -4 (y-1)

Step-by-step explanation:

Given,

Focus of parabola = (0,0)

And, directrix is, y = 2,

Thus, the parabola must be along y-axis,

We know that,

The standard form of a parabola along y-axis,

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

Where, focus = (h, k+p)

And, directrix, y = k-p

Thus, we can write,

h = 0, k+p = 0

k-p = 2

⇒ k+p + k-p = 0 + 2

⇒ 2k = 2 ⇒ k = 1

⇒ 1 - p = 2 ⇒ p = - 1

Hence, the equation of the parabola is,

(x-0)^2=4(-1)(y-1)

\implies x^2 = -4(y-1)

Option 4 is correct.

Ilya [14]3 years ago
3 0
The answer is 3 because z to the y a-1
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