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

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

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

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

(h, k) = (1, - 2), a = 2, b = 4

Solution steps

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

Rewrite

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

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

(h, k) = (1, - 2), a = 2, b = 4

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (1, - 2), b = 4, a = 2

9 x^{2} + 81 y^{2} - 729 = 0

x^{2} + 4 y^{2} - 4 x - 8 y + 3 = 0

y^{2} = 9 + \frac{- ( 5 x + 4 ) ( 5 x - 6 )}{2}

x^{2} + 4 y^{2} - 6 x + 16 y = - 9

4 x^{2} + y^{2} + 2 y - 15 = 0

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