What is 9x^2+4y^2-18x+8y+4=0 ?

The solution to 9x^2+4y^2-18x+8y+4=0 is Ellipse with (h,k)=(1,-1),a=1,b= 3/2

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9x^2+4y^2-18x+8y+4=0

9 x^{2} + 4 y^{2} - 18 x + 8 y + 4 = 0

(h, k) = (1, - 1), a = 1, b = \frac{3}{2}

Solution steps

9 x^{2} + 4 y^{2} - 18 x + 8 y + 4 = 0

Rewrite

9 x^{2} + 4 y^{2} - 18 x + 8 y + 4 = 0

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

(h, k) = (1, - 1), a = 1, b = \frac{3}{2}

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (1, - 1), b = \frac{3}{2}, a = 1

What is 9x^2+4y^2-18x+8y+4=0 ?
The solution to 9x^2+4y^2-18x+8y+4=0 is Ellipse with (h,k)=(1,-1),a=1,b= 3/2