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

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

x^{(2)} - 4 x + 3 y^{(2)} = - 2

25 x^{(2)} + 4 y^{(2)} = 84

4 x^{2} - 16 x + 9 y^{2} + 54 y = - 61

(x^{2} + 9 x + 4 y^{2} + 10 y) = 14

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