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

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

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

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

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

Solution steps

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

Rewrite

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

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

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

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

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

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

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

4 x^{2} + 24 y^{2} = 100

- x^{2} - 2 y^{2} = - 40

9 x^{2} + 16 y^{2} - 36 x - 64 y + (- 44) = 0

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