What is y^{(2)}+2y=3x-2 ?

The solution to y^{(2)}+2y=3x-2 is Parabola with (h,k)=(1/3 ,-1),p= 3/4

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

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

(h, k) = (\frac{1}{3}, - 1), p = \frac{3}{4}

Solution steps

y^{2} + 2 y = 3 x - 2

Rewrite

y^{2} + 2 y = 3 x - 2

in the standard form

4 \cdot \frac{3}{4} (x - \frac{1}{3}) = (y - (- 1))^{2}

Therefore parabola properties are:

(h, k) = (\frac{1}{3}, - 1), p = \frac{3}{4}

16 x^{2} - y = 0

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

(x + \frac{2}{5})^{2} + (y + \frac{2}{3}) = 10

3 y^{2} + 4 x - 24 y + 44 = 0

4 x^{2} + 2 y = 10

What is y^{(2)}+2y=3x-2 ?
The solution to y^{(2)}+2y=3x-2 is Parabola with (h,k)=(1/3 ,-1),p= 3/4