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

Answer:

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

Step-by-step 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.

Answer 2

Answer:

  y equals 1 divided by 24 x squared  

Step-by-step explanation:

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