What is ((x-2)^2)/9+((y+5)^2)/(36)=1 ?

The solution to ((x-2)^2)/9+((y+5)^2)/(36)=1 is Ellipse with (h,k)=(2,-5),a=3,b=6

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((x-2)^2)/9+((y+5)^2)/(36)=1

\frac{( x - 2 ) ^{2}}{9} + \frac{( y + 5 ) ^{2}}{36} = 1

(h, k) = (2, - 5), a = 3, b = 6

Solution steps

\frac{( x - 2 ) ^{2}}{9} + \frac{( y + 5 ) ^{2}}{36} = 1

Rewrite

\frac{( x - 2 ) ^{2}}{9} + \frac{( y + 5 ) ^{2}}{36} = 1

in the form of the standard ellipse equation

\frac{( x - 2 ) ^{2}}{3 ^{2}} + \frac{( y - ( - 5 ) ) ^{2}}{6 ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (2, - 5), a = 3, b = 6

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (2, - 5), b = 6, a = 3

2 y^{2} = - x^{2} + 4

16 x^{2} - 64 x + 9 y^{2} + 9 y + 1 = 0

\frac{( x + 5 ) ^{2}}{81} + \frac{( y - 1 ) ^{2}}{144} = 1

\frac{8 x}{x ^{2} + y ^{2} + 1} = 1

(16 - x^{2} - 9 y^{2}) = - 1

What is ((x-2)^2)/9+((y+5)^2)/(36)=1 ?
The solution to ((x-2)^2)/9+((y+5)^2)/(36)=1 is Ellipse with (h,k)=(2,-5),a=3,b=6