What is ((y-3)^2)/(64)+((x+5)^2)/(81)=1 ?

The solution to ((y-3)^2)/(64)+((x+5)^2)/(81)=1 is Ellipse with (h,k)=(-5,3),a=9,b=8

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((y-3)^2)/(64)+((x+5)^2)/(81)=1

\frac{( y - 3 ) ^{2}}{64} + \frac{( x + 5 ) ^{2}}{81} = 1

(h, k) = (- 5, 3), a = 9, b = 8

Solution steps

\frac{( y - 3 ) ^{2}}{64} + \frac{( x + 5 ) ^{2}}{81} = 1

Rewrite

\frac{( y - 3 ) ^{2}}{64} + \frac{( x + 5 ) ^{2}}{81} = 1

in the form of the standard ellipse equation

\frac{( x - ( - 5 ) ) ^{2}}{9 ^{2}} + \frac{( y - 3 ) ^{2}}{8 ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (- 5, 3), a = 9, b = 8

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (- 5, 3), a = 9, b = 8

4 - 4 x^{2} - y^{2} \geq 0

x^{2} + 5 y^{2} = 20

4 x^{2} + 2 y^{2} + 6 x + 8 y + 4 = 0

\frac{1 + b + ia}{1 + b - ia} = b + ia

2 x^{2} + y^{2} + 4 x - 6 y - 12 = 0

What is ((y-3)^2)/(64)+((x+5)^2)/(81)=1 ?
The solution to ((y-3)^2)/(64)+((x+5)^2)/(81)=1 is Ellipse with (h,k)=(-5,3),a=9,b=8