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

The solution to y^2+30x^2=30 is Ellipse with (h,k)=(0,0),a=1,b=sqrt(30)

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y^2+30x^2=30

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

(h, k) = (0, 0), a = 1, b = 30

Solution steps

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

Rewrite

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

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

(h, k) = (0, 0), a = 1, b = 30

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (0, 0), b = 30, a = 1

\frac{x ^{2}}{25} + \frac{( y + 3 ) ^{2}}{49} = 1

9 x^{2} + 25 y^{2} = 225

81 x^{2} - 1296 x + 16 y^{2} + 64 y = - 3952

6 x^{2} + 8 y^{2} + 12 x - 32 y = 178

49 x^{2} + 25 y^{2} - 196 x + 250 y - 404 = 0

What is y^2+30x^2=30 ?
The solution to y^2+30x^2=30 is Ellipse with (h,k)=(0,0),a=1,b=sqrt(30)