What is x^2+y^2=10-x^2-2y^2 ?

The solution to x^2+y^2=10-x^2-2y^2 is Ellipse with (h,k)=(0,0),a=sqrt(5),b=sqrt(10/3)

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x^2+y^2=10-x^2-2y^2

x^{2} + y^{2} = 10 - x^{2} - 2 y^{2}

(h, k) = (0, 0), a = 5, b = \frac{10}{3}

Solution steps

x^{2} + y^{2} = 10 - x^{2} - 2 y^{2}

Rewrite

x^{2} + y^{2} - 10 + x^{2} + 2 y^{2} = 0

in the form of the standard ellipse equation

\frac{( x - 0 ) ^{2}}{( 5 ) ^{2}} + \frac{( y - 0 ) ^{2}}{( \frac{10}{3} ) ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (0, 0), a = 5, b = \frac{10}{3}

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (0, 0), a = 5, b = \frac{10}{3}

- \frac{x ^{2}}{9} - y^{2} = 1

5 x^{2} + 72 y^{2} - 2 > 0

128 + 16 y - x^{2} - 4 y^{2} \geq 0

144 y^{2} + 169 x^{2} = 169

9 (x + y i)^{2} + 9 (x - y i)^{2} + 82 (x + y i) (x - y i) = 1600

What is x^2+y^2=10-x^2-2y^2 ?
The solution to x^2+y^2=10-x^2-2y^2 is Ellipse with (h,k)=(0,0),a=sqrt(5),b=sqrt(10/3)