What is (x^2)/9+(y^2)/4 =2 ?

The solution to (x^2)/9+(y^2)/4 =2 is Ellipse with (h,k)=(0,0),a=3sqrt(2),b=2sqrt(2)

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(x^2)/9+(y^2)/4 =2

\frac{x ^{2}}{9} + \frac{y ^{2}}{4} = 2

(h, k) = (0, 0), a = 32, b = 22

Solution steps

\frac{x ^{2}}{9} + \frac{y ^{2}}{4} = 2

Rewrite

\frac{x ^{2}}{9} + \frac{y ^{2}}{4} = 2

in the form of the standard ellipse equation

\frac{( x - 0 ) ^{2}}{( 3 2 ) ^{2}} + \frac{( y - 0 ) ^{2}}{( 2 2 ) ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (0, 0), a = 32, b = 22

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (0, 0), a = 32, b = 22

\frac{( x - 0 ) ^{2}}{1 ^{2}} + \frac{( y - 0 ) ^{2}}{3 ^{2}} = 1

2 x^{2} + 4 y^{2} + 14 x + 8 y + 16 = 0

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

\frac{x ^{2}}{9} + \frac{( y - 3 ) ^{2}}{4} = 1

x^{2} + 4 y^{2} - 6 x + 16 y = 0

What is (x^2)/9+(y^2)/4 =2 ?
The solution to (x^2)/9+(y^2)/4 =2 is Ellipse with (h,k)=(0,0),a=3sqrt(2),b=2sqrt(2)