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

The solution to (x-1)^2+4y^2=4 is Ellipse with (h,k)=(1,0),a=2,b=1

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

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

(h, k) = (1, 0), a = 2, b = 1

Solution steps

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

Rewrite

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

in the form of the standard ellipse equation

\frac{( x - 1 ) ^{2}}{2 ^{2}} + \frac{( y - 0 ) ^{2}}{1 ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (1, 0), a = 2, b = 1

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (1, 0), a = 2, b = 1

2 x^{2} + 3 y^{2} - 12 x + 12 y + 12 = 0

\frac{y ^{2}}{4} + \frac{z ^{2}}{9} = 1

2 x^{2} + y^{2} - 2 x \leq 0

\frac{( x + 7 ) ^{2}}{6} + \frac{( y + 7 ) ^{2}}{5} = 1

4 x^{2} - 16 + y^{2} + 2 y = - 1

What is (x-1)^2+4y^2=4 ?
The solution to (x-1)^2+4y^2=4 is Ellipse with (h,k)=(1,0),a=2,b=1