What is ((y+3)^2)/(81)+((x-7)^2)/(64)=1 ?

The solution to ((y+3)^2)/(81)+((x-7)^2)/(64)=1 is Ellipse with (h,k)=(7,-3),a=8,b=9

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((y+3)^2)/(81)+((x-7)^2)/(64)=1

\frac{( y + 3 ) ^{2}}{81} + \frac{( x - 7 ) ^{2}}{64} = 1

(h, k) = (7, - 3), a = 8, b = 9

Solution steps

\frac{( y + 3 ) ^{2}}{81} + \frac{( x - 7 ) ^{2}}{64} = 1

Rewrite

\frac{( y + 3 ) ^{2}}{81} + \frac{( x - 7 ) ^{2}}{64} = 1

in the form of the standard ellipse equation

\frac{( x - 7 ) ^{2}}{8 ^{2}} + \frac{( y - ( - 3 ) ) ^{2}}{9 ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (7, - 3), a = 8, b = 9

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (7, - 3), b = 9, a = 8

x^{2} + 8 y^{2} = 8

9 x^{2} + 4 y^{2} + 36 x - 8 y + 4 = 0

7 x^{2} + 2 y^{2} = 14

4 x^{2} + 25 y^{2} - 6 x + 200 y + 304 = 0

(\frac{x + 4}{3})^{2} + (\frac{y + 4}{9})^{2} = (\frac{457}{81})^{2}

What is ((y+3)^2)/(81)+((x-7)^2)/(64)=1 ?
The solution to ((y+3)^2)/(81)+((x-7)^2)/(64)=1 is Ellipse with (h,k)=(7,-3),a=8,b=9