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

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

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

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

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

Solution steps

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

Rewrite

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

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

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

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

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

\frac{x ^{2}}{12} + \frac{y ^{2}}{25} = 1

1 x^{2} + 3 y^{2} + 10 x + 10 y - 11 = 0

16 x^{(2)} + 25 y^{(2)} = 400

16 x^{2} - 160 x + 25 y^{2} + 350 y - 1225 = 0

9 x^{2} + 16 y^{2} - 18 x - 64 y = 71

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