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

36 x^{2} + 9 y^{2} + 48 x - 36 y - 72 = 0

(x - 5)^{2} + (y - 1)^{2} + (y - 1)^{2} = 14

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

\frac{( x - 3 ) ^{2}}{( 18 )} + \frac{( y + 1 ) ^{2}}{12} = 1

4 x^{2} + 8 y^{2} - 16 \cdot + 32 y + 32 = 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