What is ((x+8)^2)/(16)+((y+1)^2)/(81)=1 ?

The solution to ((x+8)^2)/(16)+((y+1)^2)/(81)=1 is Ellipse with (h,k)=(-8,-1),a=4,b=9

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((x+8)^2)/(16)+((y+1)^2)/(81)=1

\frac{( x + 8 ) ^{2}}{16} + \frac{( y + 1 ) ^{2}}{81} = 1

(h, k) = (- 8, - 1), a = 4, b = 9

Solution steps

\frac{( x + 8 ) ^{2}}{16} + \frac{( y + 1 ) ^{2}}{81} = 1

Rewrite

\frac{( x + 8 ) ^{2}}{16} + \frac{( y + 1 ) ^{2}}{81} = 1

in the form of the standard ellipse equation

\frac{( x - ( - 8 ) ) ^{2}}{4 ^{2}} + \frac{( y - ( - 1 ) ) ^{2}}{9 ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (- 8, - 1), a = 4, b = 9

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (- 8, - 1), b = 9, a = 4

\frac{( x - 12 ) ^{2}}{289} + \frac{( y - 3 ) ^{2}}{64} = 1

3 x^{2} + 6 y^{2} - 4 x + 6 y - 3 = 0

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

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

25 x^{2} + 16 y^{2} - 100 x - 96 y - 156 = 0

What is ((x+8)^2)/(16)+((y+1)^2)/(81)=1 ?
The solution to ((x+8)^2)/(16)+((y+1)^2)/(81)=1 is Ellipse with (h,k)=(-8,-1),a=4,b=9