What is ((x-5)^2)/9+((y-1)^2)/(25)=1 ?

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

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((x-5)^2)/9+((y-1)^2)/(25)=1

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

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

Solution steps

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

Rewrite

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

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

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

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

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

\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}

3 x^{2} + 12 y^{2} + 18 x - 24 y - 69 = 0

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