What is 2x^2+y^2=57 ?

The solution to 2x^2+y^2=57 is Ellipse with (h,k)=(0,0),a=sqrt(57/2),b=sqrt(57)

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2x^2+y^2=57

2 x^{2} + y^{2} = 57

(h, k) = (0, 0), a = \frac{57}{2}, b = 57

Solution steps

2 x^{2} + y^{2} = 57

Rewrite

2 x^{2} + y^{2} = 57

in the form of the standard ellipse equation

\frac{( x - 0 ) ^{2}}{( \frac{57}{2} ) ^{2}} + \frac{( y - 0 ) ^{2}}{( 57 ) ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (0, 0), a = \frac{57}{2}, b = 57

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (0, 0), b = 57, a = \frac{57}{2}

\frac{( x - 3 ) ^{2}}{49} + \frac{( y - 5 ) ^{2}}{4} = 1

8 x^{2} + 2 y^{2} - 16 x - 16 y + 8 = 0

12 x^{2} + 3 + 7 y^{2} = 5

5 x^{2} + 2 y^{2} + 12 y + 8 = 0

4 x^{2} + 5 y^{2} - 32 x + 30 y - 11 = 0

What is 2x^2+y^2=57 ?
The solution to 2x^2+y^2=57 is Ellipse with (h,k)=(0,0),a=sqrt(57/2),b=sqrt(57)