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

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

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

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

(h, k) = (1, 2), a = 5, b = 3

Solution steps

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

Rewrite

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

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

(h, k) = (1, 2), a = 5, b = 3

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (1, 2), a = 5, b = 3

16 x^{2} + 96 x + 25 y^{2} + 100 y - 156 = 0

3 x^{2} - 6 x + y^{2} + 4 y - 2 = 0

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

4 x^{2} + 25 y^{2} - 40 x + 150 y + 225 = 0

36 x^{2} + y^{2} = 36

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