What is ((x-2)^2)/4+((y+5)^2)/9 =1 ?

The solution to ((x-2)^2)/4+((y+5)^2)/9 =1 is Ellipse with (h,k)=(2,-5),a=2,b=3

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((x-2)^2)/4+((y+5)^2)/9 =1

\frac{( x - 2 ) ^{2}}{4} + \frac{( y + 5 ) ^{2}}{9} = 1

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

Solution steps

\frac{( x - 2 ) ^{2}}{4} + \frac{( y + 5 ) ^{2}}{9} = 1

Rewrite

\frac{( x - 2 ) ^{2}}{4} + \frac{( y + 5 ) ^{2}}{9} = 1

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

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

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

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

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

2 x^{2} + 3 y^{2} + 12 x - 24 y + 60 = 0

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

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

4 x^{2} + 25 y^{2} - 24 x + 250 y + 561 = 0

What is ((x-2)^2)/4+((y+5)^2)/9 =1 ?
The solution to ((x-2)^2)/4+((y+5)^2)/9 =1 is Ellipse with (h,k)=(2,-5),a=2,b=3