What is ((x+0)^2)/(225/25)+((y-1)^2)/(225/9)=1 ?

The solution to ((x+0)^2)/(225/25)+((y-1)^2)/(225/9)=1 is Ellipse with (h,k)=(0,1),a=3,b=5

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((x+0)^2)/(225/25)+((y-1)^2)/(225/9)=1

\frac{( x + 0 ) ^{2}}{\frac{225}{25}} + \frac{( y - 1 ) ^{2}}{\frac{225}{9}} = 1

(h, k) = (0, 1), a = 3, b = 5

Solution steps

\frac{( x + 0 ) ^{2}}{\frac{225}{25}} + \frac{( y - 1 ) ^{2}}{\frac{225}{9}} = 1

Rewrite

\frac{( x + 0 ) ^{2}}{\frac{225}{25}} + \frac{( y - 1 ) ^{2}}{\frac{225}{9}} = 1

in the form of the standard ellipse equation

\frac{( x - 0 ) ^{2}}{3 ^{2}} + \frac{( y - 1 ) ^{2}}{5 ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (0, 1), a = 3, b = 5

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (0, 1), b = 5, a = 3

3 = x^{2} + 9 y^{2}

\frac{( x - 1 ) ^{2}}{16} + \frac{y ^{2}}{9} = 1

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

y^{2} - 4 y + x^{2} = 0

9 x^{2} - 72 x + y^{2} + 10 y + 160 = 0

What is ((x+0)^2)/(225/25)+((y-1)^2)/(225/9)=1 ?
The solution to ((x+0)^2)/(225/25)+((y-1)^2)/(225/9)=1 is Ellipse with (h,k)=(0,1),a=3,b=5