What is ((x+9)^2}{81}+\frac{(y-1)^2)/9 =1 ?

The solution to ((x+9)^2}{81}+\frac{(y-1)^2)/9 =1 is Ellipse with (h,k)=(-9,1),a=9,b=3

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((x+9)^2}{81}+\frac{(y-1)^2)/9 =1

\frac{( x + 9 ) ^{2}}{81} + \frac{( y - 1 ) ^{2}}{9} = 1

(h, k) = (- 9, 1), a = 9, b = 3

Solution steps

\frac{( x + 9 ) ^{2}}{81} + \frac{( y - 1 ) ^{2}}{9} = 1

Rewrite

\frac{( x + 9 ) ^{2}}{81} + \frac{( y - 1 ) ^{2}}{9} = 1

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

(h, k) = (- 9, 1), a = 9, b = 3

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (- 9, 1), a = 9, b = 3

9 x^{2} + 25 y^{2} - 36 x + 50 y - 200 = 0

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

7 x^{2} + 16 y^{2} - 112 = 0

(x - h)^{2} + (y - k)^{2} = 1

9 x^{2} + 64 y^{2} = 1

What is ((x+9)^2}{81}+\frac{(y-1)^2)/9 =1 ?
The solution to ((x+9)^2}{81}+\frac{(y-1)^2)/9 =1 is Ellipse with (h,k)=(-9,1),a=9,b=3