What is (x-4)^2+((y-2)^2)/9 =1 ?

The solution to (x-4)^2+((y-2)^2)/9 =1 is Ellipse with (h,k)=(4,2),a=1,b=3

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(x-4)^2+((y-2)^2)/9 =1

(x - 4)^{2} + \frac{( y - 2 ) ^{2}}{9} = 1

(h, k) = (4, 2), a = 1, b = 3

Solution steps

(x - 4)^{2} + \frac{( y - 2 ) ^{2}}{9} = 1

Rewrite

(x - 4)^{2} + \frac{( y - 2 ) ^{2}}{9} = 1

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

(h, k) = (4, 2), a = 1, b = 3

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (4, 2), b = 3, a = 1

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What is (x-4)^2+((y-2)^2)/9 =1 ?
The solution to (x-4)^2+((y-2)^2)/9 =1 is Ellipse with (h,k)=(4,2),a=1,b=3