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

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

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

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

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

Solution steps

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

Rewrite

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

9 x^{2} + 4 y^{2} - 18 x + 24 y = 36

9 > x^{2} + 9 y^{2}

27 x^{2} + 6 y^{2} - 5 = 0

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

\frac{u + v}{u ^{2} + v ^{2}} + \frac{- v + u}{u ^{2} + v ^{2}} = 1

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