What is ((x-1)^2)/5+((y-2)^2)/8 =1 ?

The solution to ((x-1)^2)/5+((y-2)^2)/8 =1 is Ellipse with (h,k)=(1,2),a=sqrt(5),b=2sqrt(2)

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((x-1)^2)/5+((y-2)^2)/8 =1

\frac{( x - 1 ) ^{2}}{5} + \frac{( y - 2 ) ^{2}}{8} = 1

(h, k) = (1, 2), a = 5, b = 22

Solution steps

\frac{( x - 1 ) ^{2}}{5} + \frac{( y - 2 ) ^{2}}{8} = 1

Rewrite

\frac{( x - 1 ) ^{2}}{5} + \frac{( y - 2 ) ^{2}}{8} = 1

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

(h, k) = (1, 2), a = 5, b = 22

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (1, 2), b = 22, a = 5

What is ((x-1)^2)/5+((y-2)^2)/8 =1 ?
The solution to ((x-1)^2)/5+((y-2)^2)/8 =1 is Ellipse with (h,k)=(1,2),a=sqrt(5),b=2sqrt(2)