What is -6y=x^2+y^2 ?

The solution to -6y=x^2+y^2 is Ellipse with (h,k)=(0,-3),a=3,b=3

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-6y=x^2+y^2

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

(h, k) = (0, - 3), a = 3, b = 3

Solution steps

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

Rewrite

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

in the form of the standard ellipse equation

\frac{( x - 0 ) ^{2}}{3 ^{2}} + \frac{( y - ( - 3 ) ) ^{2}}{3 ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (0, - 3), a = 3, b = 3

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (0, - 3), b = 3, a = 3

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

64 x^{2} + y^{2} = 64

- x^{2} - 2 y^{2} = 1

4 x^{2} + 7 y^{2} \leq 2

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

What is -6y=x^2+y^2 ?
The solution to -6y=x^2+y^2 is Ellipse with (h,k)=(0,-3),a=3,b=3