What are the solutions to the equation solvefor y,y^2-x^2+4x+8y+12=0 ?

The solutions to the equation solvefor y,y^2-x^2+4x+8y+12=0 are y=x-6,y=-x-2

Find the zeros of solvefor y,y^2-x^2+4x+8y+12=0

The zeros of solvefor y,y^2-x^2+4x+8y+12=0 are y=x-6,y=-x-2

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solve for

y, y^{2} - x^{2} + 4 x + 8 y + 12 = 0

y = x - 6, y = - x - 2

Solution steps

y^{2} - x^{2} + 4 x + 8 y + 12 = 0

Write in the standard form

a x^{2} + b x + c = 0

y^{2} + 8 y - x^{2} + 4 x + 12 = 0

Solve with the quadratic formula

y_{1, 2} = \frac{- 8 \pm 8 ^{2} - 4 \cdot 1 \cdot ( - x ^{2} + 4 x + 12 )}{2 \cdot 1}

Simplify

8^{2} - 4 \cdot 1 \cdot (- x^{2} + 4 x + 12) : 2 (x - 2)

y_{1, 2} = \frac{- 8 \pm 2 ( x - 2 )}{2 \cdot 1}

Separate the solutions

y_{1} = \frac{- 8 + 2 ( x - 2 )}{2 \cdot 1}, y_{2} = \frac{- 8 - 2 ( x - 2 )}{2 \cdot 1}

y = \frac{- 8 + 2 ( x - 2 )}{2 \cdot 1} : x - 6

y = \frac{- 8 - 2 ( x - 2 )}{2 \cdot 1} : - x - 2

The solutions to the quadratic equation are:

y = x - 6, y = - x - 2

- 2 x^{2}

x^{2} + y = 4

f (x) = - x^{2} + 4

x^{2} + y^{2} = 9

3 x^{2} - 8 y^{2} + 12 x + 16 y + 20 = 0

What are the solutions to the equation solvefor y,y^2-x^2+4x+8y+12=0 ?
The solutions to the equation solvefor y,y^2-x^2+4x+8y+12=0 are y=x-6,y=-x-2
Find the zeros of solvefor y,y^2-x^2+4x+8y+12=0
The zeros of solvefor y,y^2-x^2+4x+8y+12=0 are y=x-6,y=-x-2