What is 2x^2+y^2=50 ?

The solution to 2x^2+y^2=50 is Ellipse with (h,k)=(0,0),a=5,b=5sqrt(2)

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2x^2+y^2=50

2 x^{2} + y^{2} = 50

(h, k) = (0, 0), a = 5, b = 52

Solution steps

2 x^{2} + y^{2} = 50

Rewrite

2 x^{2} + y^{2} = 50

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

(h, k) = (0, 0), a = 5, b = 52

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (0, 0), b = 52, a = 5

9 x^{2} + 5 y^{2} + 18 x + 10 y - 31 = 0

x^{2} + 5 y^{2} + 10 y + 4 x - 27 = 0

x^{2} + 4 y^{2} \geq 100

4 x^{2} + 9 y^{2} + 32 x - 18 y + 37 = 0

9 x^{2} + 6 y^{2} + 36 y = 0

What is 2x^2+y^2=50 ?
The solution to 2x^2+y^2=50 is Ellipse with (h,k)=(0,0),a=5,b=5sqrt(2)