What is x^2+2y^2=30 ?

The solution to x^2+2y^2=30 is Ellipse with (h,k)=(0,0),a=sqrt(30),b=sqrt(15)

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x^2+2y^2=30

x^{2} + 2 y^{2} = 30

(h, k) = (0, 0), a = 30, b = 15

Solution steps

x^{2} + 2 y^{2} = 30

Rewrite

x^{2} + 2 y^{2} = 30

in the form of the standard ellipse equation

\frac{( x - 0 ) ^{2}}{( 30 ) ^{2}} + \frac{( y - 0 ) ^{2}}{( 15 ) ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (0, 0), a = 30, b = 15

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (0, 0), a = 30, b = 15

4 x^{2} + 16 y^{2} + 32 y = 0

\frac{( x - 4 ) ^{2}}{9} + \frac{( y + 6 ) ^{2}}{121} = 1

36 x^{2} + 16 y^{2} + 180 x - 24 y + 90 = 0

2.4 x^{2} + 4 y^{2} + 40 x - 32 y - 5 = 0

25 x^{2} + 16 y^{2} + 100 x - 32 y - 284 = 0

What is x^2+2y^2=30 ?
The solution to x^2+2y^2=30 is Ellipse with (h,k)=(0,0),a=sqrt(30),b=sqrt(15)