What is 2x^2+5y^2=10 ?

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

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2x^2+5y^2=10

2 x^{2} + 5 y^{2} = 10

(h, k) = (0, 0), a = 5, b = 2

Solution steps

2 x^{2} + 5 y^{2} = 10

Rewrite

2 x^{2} + 5 y^{2} = 10

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

(h, k) = (0, 0), a = 5, b = 2

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (0, 0), a = 5, b = 2

x^{2} + 36 y^{2} - 16 x - 72 y + 64 = 0

x^{2} + 9 y^{2} + 8 x - 36 y + 43 = 0

\frac{( x + 7 ) ^{2}}{25} + \frac{( y - 3 ) ^{2}}{4} = 1

\frac{( x - 1 ) ^{2}}{25} + \frac{( y - 2 ) ^{2}}{9} = 1

16 x^{2} + 96 x + 25 y^{2} + 100 y - 156 = 0

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