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

The solution to 2x^2+y^2-4x+8y-4=0 is Ellipse with (h,k)=(1,-4),a=sqrt(11),b=sqrt(22)

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

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

(h, k) = (1, - 4), a = 11, b = 22

Solution steps

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

Rewrite

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

in the form of the standard ellipse equation

\frac{( x - 1 ) ^{2}}{( 11 ) ^{2}} + \frac{( y - ( - 4 ) ) ^{2}}{( 22 ) ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (1, - 4), a = 11, b = 22

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (1, - 4), b = 22, a = 11

25 x^{2} + 9 y^{2} - 250 x - 18 y + 409 = 0

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

\frac{( x - 1 ) ^{2}}{6} + \frac{( y - 3 ) ^{2}}{2} = 1

\frac{12 ( x ) ^{2}}{24} + \frac{3 y ^{2}}{24} = \frac{24}{24}

\frac{( x - 1 ) ^{2}}{16} + \frac{( y + 2 ) ^{2}}{9} = 1

What is 2x^2+y^2-4x+8y-4=0 ?
The solution to 2x^2+y^2-4x+8y-4=0 is Ellipse with (h,k)=(1,-4),a=sqrt(11),b=sqrt(22)