What is ((x-(-2))^2)/9+((y-3)^2)/(25)=1 ?

The solution to ((x-(-2))^2)/9+((y-3)^2)/(25)=1 is Ellipse with (h,k)=(-2,3),a=3,b=5

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((x-(-2))^2)/9+((y-3)^2)/(25)=1

\frac{( x - ( - 2 ) ) ^{2}}{9} + \frac{( y - 3 ) ^{2}}{25} = 1

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

Solution steps

\frac{( x - ( - 2 ) ) ^{2}}{9} + \frac{( y - 3 ) ^{2}}{25} = 1

Rewrite

\frac{( x - ( - 2 ) ) ^{2}}{9} + \frac{( y - 3 ) ^{2}}{25} = 1

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

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

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

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

(\frac{x ^{2}}{15}) + (\frac{( y - 8 ) ^{2}}{49}) = 1

20 x^{2} + 40 y^{2} = 800

8 x^{2} + 3 y^{2} = 24

\frac{( x - 4 ) ^{2}}{9} + \frac{( y + 6 ) ^{2}}{4} = 1

9 x^{2} + 4 y^{2} + 18 x + 32 y + 37 = 0

What is ((x-(-2))^2)/9+((y-3)^2)/(25)=1 ?
The solution to ((x-(-2))^2)/9+((y-3)^2)/(25)=1 is Ellipse with (h,k)=(-2,3),a=3,b=5