What is 2x^2+7y^2=14 ?

The solution to 2x^2+7y^2=14 is Ellipse with (h,k)=(0,0),a=sqrt(7),b=sqrt(2)

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2x^2+7y^2=14

2 x^{2} + 7 y^{2} = 14

(h, k) = (0, 0), a = 7, b = 2

Solution steps

2 x^{2} + 7 y^{2} = 14

Rewrite

2 x^{2} + 7 y^{2} = 14

in the form of the standard ellipse equation

\frac{( x - 0 ) ^{2}}{( 7 ) ^{2}} + \frac{( y - 0 ) ^{2}}{( 2 ) ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (0, 0), a = 7, b = 2

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (0, 0), a = 7, b = 2

\frac{( x - 2 ) ^{2}}{36} + \frac{( y + 1 ) ^{2}}{25} = 1

x^{2} + (\frac{y ^{2}}{4}) = 1

4 = 4 x^{2} + y^{2} + 1

\frac{( x + 4 ) ^{2}}{25} + \frac{( y - 2 ) ^{2}}{9} = 1

\frac{x ^{2}}{1} + \frac{y ^{2}}{15} = 1

What is 2x^2+7y^2=14 ?
The solution to 2x^2+7y^2=14 is Ellipse with (h,k)=(0,0),a=sqrt(7),b=sqrt(2)