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

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

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

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

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

Solution steps

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

Rewrite

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

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

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

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

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

(2 x + 3)^{2} + (y - 2)^{2} = 26

4 x^{2} + y^{2} - 32 x + 4 y + 64 = 0

\frac{x ^{2}}{289} + \frac{y ^{2}}{225} = 1

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

4 x^{2} + y^{2} = 2 y + 3

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