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x^{2}=18-y^{2}
Subtract y^{2} from both sides.
x=\sqrt{18-y^{2}} x=-\sqrt{18-y^{2}}
Take the square root of both sides of the equation.
x^{2}+y^{2}-18=0
Subtract 18 from both sides.
x=\frac{0±\sqrt{0^{2}-4\left(y^{2}-18\right)}}{2}
This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and y^{2}-18 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.
x=\frac{0±\sqrt{-4\left(y^{2}-18\right)}}{2}
Square 0.
x=\frac{0±\sqrt{72-4y^{2}}}{2}
Multiply -4 times y^{2}-18.
x=\frac{0±2\sqrt{18-y^{2}}}{2}
Take the square root of -4y^{2}+72.
x=\sqrt{18-y^{2}}
Now solve the equation x=\frac{0±2\sqrt{18-y^{2}}}{2} when ± is plus.
x=-\sqrt{18-y^{2}}
Now solve the equation x=\frac{0±2\sqrt{18-y^{2}}}{2} when ± is minus.
x=\sqrt{18-y^{2}} x=-\sqrt{18-y^{2}}
The equation is now solved.
y^{2}=18-x^{2}
Subtract x^{2} from both sides.
y=\sqrt{18-x^{2}} y=-\sqrt{18-x^{2}}
Take the square root of both sides of the equation.
x^{2}+y^{2}-18=0
Subtract 18 from both sides.
y^{2}+x^{2}-18=0
Quadratic equations like this one, with an x^{2} term but no x term, can still be solved using the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}, once they are put in standard form: ax^{2}+bx+c=0.
y=\frac{0±\sqrt{0^{2}-4\left(x^{2}-18\right)}}{2}
This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and x^{2}-18 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.
y=\frac{0±\sqrt{-4\left(x^{2}-18\right)}}{2}
Square 0.
y=\frac{0±\sqrt{72-4x^{2}}}{2}
Multiply -4 times x^{2}-18.
y=\frac{0±2\sqrt{18-x^{2}}}{2}
Take the square root of -4x^{2}+72.
y=\sqrt{18-x^{2}}
Now solve the equation y=\frac{0±2\sqrt{18-x^{2}}}{2} when ± is plus.
y=-\sqrt{18-x^{2}}
Now solve the equation y=\frac{0±2\sqrt{18-x^{2}}}{2} when ± is minus.
y=\sqrt{18-x^{2}} y=-\sqrt{18-x^{2}}
The equation is now solved.