Question

Find the standard form of the equation of the parabola with a focus at (0, 6) and a directrix at y = -6.

A) y equals 1 divided by 24 x squared

B) y2 = 6x

C) y2 = 24x

D) y equals 1 divided by 6 x squared

Answer 1

y equals 1 divided by 24 x squared

Explanation:

Just took the test

Answer 2

None of the options represent the right answer. (Real answer:
`y = 24\cdot x^(2)`)

Explanation:

The parabola shown above is vertical and least distance between focus and directrix is equal to
`2\cdot p`. Then, the value of p is determined with the help of the Pythagorean Theorem:

`2\cdot p = \sqrt{(0-0)^(2)+[6-(-6)]^(2)}`

`2\cdot p = 12`

`p = 6`

The general equation of a parabola centered at (h,k) is:

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

It is evident that parabola is centered at origin. Hence, the equation of the parabola in standard form is:

`y = 24\cdot x^(2)`

None of the options represent the right answer.