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

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

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

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

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

Solution steps

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

Rewrite

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

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

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

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

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

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

\frac{( x ^{2} )}{16} + \frac{( y ^{2} )}{9} = 1

- 1 = x^{2} + y^{2}

\frac{x ^{2}}{9} + \frac{y ^{2}}{20} = 1

\frac{x ^{2} + y ^{2} + 8 y - 16}{x ^{2} + y ^{2} + 8 y + 16} = 9

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