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

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

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

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

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

Solution steps

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

Rewrite

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

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

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

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

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

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2 x^{2} + 9 y^{2} - 12 x - 18 y + 9 = 0

\frac{x ^{2}}{100} + \frac{y ^{2}}{144} = 1

3 x^{2} + 2 y^{2} - 17 x = 0

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