What is x^2-8x+2y^2+8y=20 ?

The solution to x^2-8x+2y^2+8y=20 is Ellipse with (h,k)=(4,-2),a=2sqrt(11),b=sqrt(22)

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x^2-8x+2y^2+8y=20

x^{2} - 8 x + 2 y^{2} + 8 y = 20

(h, k) = (4, - 2), a = 211, b = 22

Solution steps

x^{2} - 8 x + 2 y^{2} + 8 y = 20

Rewrite

x^{2} - 8 x + 2 y^{2} + 8 y = 20

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

(h, k) = (4, - 2), a = 211, b = 22

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (4, - 2), a = 211, b = 22

x^{2} + 36 y^{2} - 24 x - 288 y + 611 = 0

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3 x^{2} + 4 y^{2} + 28 x - 16 y + 48 = 0

6 x^{2} + y^{2} - 12 x + 2 y = 1

(x - 5)^{2} + (y + 8)^{2} + (x - 3)^{2} - 98 = 0

What is x^2-8x+2y^2+8y=20 ?
The solution to x^2-8x+2y^2+8y=20 is Ellipse with (h,k)=(4,-2),a=2sqrt(11),b=sqrt(22)