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

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

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

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

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

Solution steps

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

Therefore ellipse properties are:

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

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

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

\frac{( x - 5 ) ^{2}}{9} + \frac{( y - 1 ) ^{2}}{25} = 1

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

16 x^{2} - 96 x + 9 y^{2} = 0

20 (x + 1)^{2} + 9 y^{2} = 180

x^{2} + 5 y^{2} = \frac{1}{5}

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