What is ((x-1)^2)/5+((y-3)^2)/4 =1 ?

The solution to ((x-1)^2)/5+((y-3)^2)/4 =1 is Ellipse with (h,k)=(1,3),a=sqrt(5),b=2

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((x-1)^2)/5+((y-3)^2)/4 =1

\frac{( x - 1 ) ^{2}}{5} + \frac{( y - 3 ) ^{2}}{4} = 1

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

Solution steps

\frac{( x - 1 ) ^{2}}{5} + \frac{( y - 3 ) ^{2}}{4} = 1

Rewrite

\frac{( x - 1 ) ^{2}}{5} + \frac{( y - 3 ) ^{2}}{4} = 1

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

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

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

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

9 x^{2} + 4 y^{2} - 126 x - 40 y + 505 = 0

\frac{( x + 2 ) ^{2}}{16} + \frac{( y - 3 ) ^{2}}{25} = 1

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

\frac{y ^{2}}{4 - x ^{2}} = 1

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

What is ((x-1)^2)/5+((y-3)^2)/4 =1 ?
The solution to ((x-1)^2)/5+((y-3)^2)/4 =1 is Ellipse with (h,k)=(1,3),a=sqrt(5),b=2