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=sqrt(3),b=2sqrt(3)

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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 = 3, b = 23

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}}{( 3 ) ^{2}} + \frac{( y - ( - 2 ) ) ^{2}}{( 2 3 ) ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (1, - 2), a = 3, b = 23

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (1, - 2), b = 23, a = 3

x^{2} + 4 y^{2} - 6 x - 16 y + 21 > 0

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

\frac{( x - 2 ) ^{2}}{2} + \frac{( y - 1 ) ^{2}}{8} = 1

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

\frac{X ^{2}}{27} + \frac{Y ^{2}}{36} = 1

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=sqrt(3),b=2sqrt(3)