What is 4x^2+y^2+8x-4y+4=0 ?

The solution to 4x^2+y^2+8x-4y+4=0 is Ellipse with (h,k)=(-1,2),a=1,b=2

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4x^2+y^2+8x-4y+4=0

4 x^{2} + y^{2} + 8 x - 4 y + 4 = 0

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

Solution steps

4 x^{2} + y^{2} + 8 x - 4 y + 4 = 0

Rewrite

4 x^{2} + y^{2} + 8 x - 4 y + 4 = 0

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

y, y^{2} = x^{2}

y^{2} - 5 y - x + 7 = 0

\frac{x ^{2}}{4} - \frac{y ^{2}}{16} = 1

2 x^{2} - y^{2} = 4

4 x^{2} + y^{2} - 8 x + 4 y - 8 = 0

What is 4x^2+y^2+8x-4y+4=0 ?
The solution to 4x^2+y^2+8x-4y+4=0 is Ellipse with (h,k)=(-1,2),a=1,b=2