What is ((d^2y))/(dx^2)-a=0 ?

The solution to ((d^2y))/(dx^2)-a=0 is Parabola with (h,k)=(0,0),p= 1/(4a)

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((d^2y))/(dx^2)-a=0

\frac{( d ^{2} y )}{d x ^{2}} - a = 0

(h, k) = (0, 0), p = \frac{1}{4 a}

Solution steps

\frac{d ^{2} y}{d x ^{2}} - a = 0

Rewrite

\frac{d ^{2} y}{d x ^{2}} - a = 0

in the standard form

4 \cdot \frac{1}{4 a} (y - 0) = (x - 0)^{2}

Therefore parabola properties are:

(h, k) = (0, 0), p = \frac{1}{4 a}

(x + 3)^{2} = - 8 (y - 3)

(y - 1)^{2} = 8 (x - 1)

(x - 1)^{2} = - 20 (y - 4)

x^{2} + 6 x + 9 y - 27 = 0

y^{2} - 8 x - 4 y - 20 = 0

What is ((d^2y))/(dx^2)-a=0 ?
The solution to ((d^2y))/(dx^2)-a=0 is Parabola with (h,k)=(0,0),p= 1/(4a)