What is ((x+6)^2}{18}+\frac{(y+3)^2)/9 =1 ?

The solution to ((x+6)^2}{18}+\frac{(y+3)^2)/9 =1 is Ellipse with (h,k)=(-6,-3),a=3sqrt(2),b=3

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((x+6)^2}{18}+\frac{(y+3)^2)/9 =1

\frac{( x + 6 ) ^{2}}{18} + \frac{( y + 3 ) ^{2}}{9} = 1

(h, k) = (- 6, - 3), a = 32, b = 3

Solution steps

\frac{( x + 6 ) ^{2}}{18} + \frac{( y + 3 ) ^{2}}{9} = 1

Rewrite

\frac{( x + 6 ) ^{2}}{18} + \frac{( y + 3 ) ^{2}}{9} = 1

in the form of the standard ellipse equation

\frac{( x - ( - 6 ) ) ^{2}}{( 3 2 ) ^{2}} + \frac{( y - ( - 3 ) ) ^{2}}{3 ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (- 6, - 3), a = 32, b = 3

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (- 6, - 3), a = 32, b = 3

3 x^{2} + 3 y^{2} - 36 y = 0

4 x^{2} + 8 y^{2} - 4 x - 24 y - 13 = 0

x^{2} + 16 y^{2} - 2 x - 64 y + 49 = 0

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

\frac{( x - 5 ) ^{2}}{2 ^{2}} + \frac{( y - 3 ) ^{2}}{9} = 1

What is ((x+6)^2}{18}+\frac{(y+3)^2)/9 =1 ?
The solution to ((x+6)^2}{18}+\frac{(y+3)^2)/9 =1 is Ellipse with (h,k)=(-6,-3),a=3sqrt(2),b=3