What is ((x+2)^2}{36}+\frac{(y+5)^2)/9 =1 ?

The solution to ((x+2)^2}{36}+\frac{(y+5)^2)/9 =1 is Ellipse with (h,k)=(-2,-5),a=6,b=3

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((x+2)^2}{36}+\frac{(y+5)^2)/9 =1

\frac{( x + 2 ) ^{2}}{36} + \frac{( y + 5 ) ^{2}}{9} = 1

(h, k) = (- 2, - 5), a = 6, b = 3

Solution steps

\frac{( x + 2 ) ^{2}}{36} + \frac{( y + 5 ) ^{2}}{9} = 1

Rewrite

\frac{( x + 2 ) ^{2}}{36} + \frac{( y + 5 ) ^{2}}{9} = 1

in the form of the standard ellipse equation

\frac{( x - ( - 2 ) ) ^{2}}{6 ^{2}} + \frac{( y - ( - 5 ) ) ^{2}}{3 ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (- 2, - 5), a = 6, b = 3

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (- 2, - 5), a = 6, b = 3

\frac{x ^{2}}{9} + \frac{y ^{2}}{4} = 1 \cdot \frac{1}{9} \cdot \frac{1}{4}

16 x^{2} + 9 y^{2} - 32 x + 18 y - 119 = 0

16 x^{2} + 36 y^{2} + 112 x - 108 y + 133 = 0

2 x^{2} + 11 y^{2} = 11

2 x^{2} + 3 y^{2} = 11

What is ((x+2)^2}{36}+\frac{(y+5)^2)/9 =1 ?
The solution to ((x+2)^2}{36}+\frac{(y+5)^2)/9 =1 is Ellipse with (h,k)=(-2,-5),a=6,b=3