x^2=-6y

Solution

x^{2} = - 6 y

(h, k) = (0, 0), p = - \frac{3}{2}

Solution steps

x^{2} = - 6 y

Rewrite

x^{2} = - 6 y

in the standard form:

4 (- \frac{3}{2}) (y - 0) = (x - 0)^{2}

Therefore parabola properties are:

(h, k) = (0, 0), p = - \frac{3}{2}

y^{2} - 4 y - 4 x = 0

\frac{x ^{2}}{16} + \frac{y ^{2}}{49} = 1

\frac{x ^{2}}{25} + \frac{y ^{2}}{25} = 1

\frac{y ^{2}}{64} - \frac{x ^{2}}{36} = 1

\frac{( x - 1 ) ^{2}}{25} - \frac{( y + 3 ) ^{2}}{9} = 1