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

25 x^{2} + 9 y^{2} - 18 y - 216 = 0

\frac{x ^{2}}{63500} + \frac{y ^{2}}{50900} = 1

4 x^{2} + 9 y^{2} + 24 x - 36 y + 36 = 0

9 x^{2} + 16 y^{2} - 36 x + 96 y + 36 = 0

x^{2} - 4 x + 3 y^{2} + y = 12

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