What is x^2-2x+2y^2-8y+7=0 ?

The solution to x^2-2x+2y^2-8y+7=0 is Ellipse with (h,k)=(1,2),a=sqrt(2),b=1

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x^2-2x+2y^2-8y+7=0

x^{2} - 2 x + 2 y^{2} - 8 y + 7 = 0

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

Solution steps

x^{2} - 2 x + 2 y^{2} - 8 y + 7 = 0

Rewrite

x^{2} - 2 x + 2 y^{2} - 8 y + 7 = 0

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

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

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

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

x^{2} + 16 y^{2} = 1

9 x^{2} + 4 y^{2} - 36 x + 24 y + 36 = 0

25 x^{2} + 9 y^{2} - 150 x - 36 y = - 36

y^{2} = 4 - 4 x^{2}

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

What is x^2-2x+2y^2-8y+7=0 ?
The solution to x^2-2x+2y^2-8y+7=0 is Ellipse with (h,k)=(1,2),a=sqrt(2),b=1