What is y+x^2-2x^2+12y-12=0 ?

The solution to y+x^2-2x^2+12y-12=0 is Parabola with (h,k)=(0, 12/13),p= 13/4

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y+x^2-2x^2+12y-12=0

y + x^{2} - 2 x^{2} + 12 y - 12 = 0

(h, k) = (0, \frac{12}{13}), p = \frac{13}{4}

Solution steps

y + x^{2} - 2 x^{2} + 12 y - 12 = 0

Rewrite

y + x^{2} - 2 x^{2} + 12 y - 12 = 0

in the standard form:

4 \cdot \frac{13}{4} (y - \frac{12}{13}) = (x - 0)^{2}

Therefore parabola properties are:

(h, k) = (0, \frac{12}{13}), p = \frac{13}{4}

(x - 3)^{2} = y - 7

- 2 = y - 3 x^{2} + 4 x

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

5 X^{2} + 4 X - 3 (3 Y - 8) + 6 = - 2 (5 X - 5)

y > - 4 x^{2} - 12 x - 8

What is y+x^2-2x^2+12y-12=0 ?
The solution to y+x^2-2x^2+12y-12=0 is Parabola with (h,k)=(0, 12/13),p= 13/4