What is x^2+2y^2-2x+8y+5=0 ?

The solution to x^2+2y^2-2x+8y+5=0 is Ellipse with (h,k)=(1,-2),a=2,b=sqrt(2)

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x^2+2y^2-2x+8y+5=0

x^{2} + 2 y^{2} - 2 x + 8 y + 5 = 0

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

Solution steps

x^{2} + 2 y^{2} - 2 x + 8 y + 5 = 0

Rewrite

x^{2} + 2 y^{2} - 2 x + 8 y + 5 = 0

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

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

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

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

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

x^{2} + y^{2} = 5

\frac{x ^{2}}{36} - \frac{y ^{2}}{4} = 1

5 x^{2} + 30 x + 24 y = 51

y^{2} - 12 y - 4 x + 28 = 0

What is x^2+2y^2-2x+8y+5=0 ?
The solution to x^2+2y^2-2x+8y+5=0 is Ellipse with (h,k)=(1,-2),a=2,b=sqrt(2)