What is (x^2)/9+(y^2)/4 =y+6 ?

The solution to (x^2)/9+(y^2)/4 =y+6 is Ellipse with (h,k)=(0,2),a=3sqrt(7),b=2sqrt(7)

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(x^2)/9+(y^2)/4 =y+6

\frac{x ^{2}}{9} + \frac{y ^{2}}{4} = y + 6

(h, k) = (0, 2), a = 37, b = 27

Solution steps

\frac{x ^{2}}{9} + \frac{y ^{2}}{4} = y + 6

Rewrite

\frac{x ^{2}}{9} + \frac{y ^{2}}{4} = y + 6

in the form of the standard ellipse equation

\frac{( x - 0 ) ^{2}}{( 3 7 ) ^{2}} + \frac{( y - 2 ) ^{2}}{( 2 7 ) ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (0, 2), a = 37, b = 27

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (0, 2), a = 37, b = 27

What is (x^2)/9+(y^2)/4 =y+6 ?
The solution to (x^2)/9+(y^2)/4 =y+6 is Ellipse with (h,k)=(0,2),a=3sqrt(7),b=2sqrt(7)