Question

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Derive the equation of the parabola with a focus at (0, −4) and a directrix of y = 4.

f(x) = −16x^2

f(x) = 16x^2

f(x) = −1/16 x^2

f(x) = 1/16 x^2

Answer 1

I am thinking C

Answer 2

f(x) = −1/16 x^2

Answer 3

\[\sqrt{\left( x-0 \right)^{2}+\left( y+4 \right)^{2}}=\frac{ \left| y-4 \right| }{ \sqrt{0^{2}+1^{2}} }\]
squaring both sides
\[x ^{2}+y ^{2}+8y+16=y ^{2}-8y+16\]
\[x ^{2}=-16 y \]
which is the required equation.