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

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

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

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

(h, k) = (1, - 3), a = 3, b = 5

Solution steps

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

Rewrite

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

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

(h, k) = (1, - 3), a = 3, b = 5

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (1, - 3), b = 5, a = 3

\frac{x ^{2}}{81} + \frac{y ^{2}}{36} = 1

x^{2} + 25 y^{2} - 200 y + 375 = 0

\frac{( x + 1 ) ^{2}}{36} + \frac{( y + 3 ) ^{2}}{25} = 1

x^{2} + 9 y^{2} + 2 x - 18 y + 1 = 0

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

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