What is x^2+10y^2-6x+20y+18=0 ?

The solution to x^2+10y^2-6x+20y+18=0 is Ellipse with (h,k)=(3,-1),a=1,b=sqrt(1/10)

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x^2+10y^2-6x+20y+18=0

x^{2} + 10 y^{2} - 6 x + 20 y + 18 = 0

(h, k) = (3, - 1), a = 1, b = \frac{1}{10}

Solution steps

x^{2} + 10 y^{2} - 6 x + 20 y + 18 = 0

Rewrite

x^{2} + 10 y^{2} - 6 x + 20 y + 18 = 0

in the form of the standard ellipse equation

\frac{( x - 3 ) ^{2}}{1 ^{2}} + \frac{( y - ( - 1 ) ) ^{2}}{( \frac{1}{10} ) ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (3, - 1), a = 1, b = \frac{1}{10}

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (3, - 1), a = 1, b = \frac{1}{10}

\frac{( x - 1 ) ^{2}}{7 ^{2}} + \frac{( y - 1 ) ^{2}}{3 ^{2}} = 1

\frac{( x - 1 ) ^{2}}{36} + \frac{( y + 2 ) ^{2}}{25} = 1

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

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

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

What is x^2+10y^2-6x+20y+18=0 ?
The solution to x^2+10y^2-6x+20y+18=0 is Ellipse with (h,k)=(3,-1),a=1,b=sqrt(1/10)