What is 9x^2+4y^2-36x+8y+31=0 ?

The solution to 9x^2+4y^2-36x+8y+31=0 is Ellipse with (h,k)=(2,-1),a=1,b= 3/2

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9x^2+4y^2-36x+8y+31=0

9 x^{2} + 4 y^{2} - 36 x + 8 y + 31 = 0

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

Solution steps

9 x^{2} + 4 y^{2} - 36 x + 8 y + 31 = 0

Rewrite

9 x^{2} + 4 y^{2} - 36 x + 8 y + 31 = 0

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

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

\frac{x ^{2}}{1.586 9 ^{2}} + \frac{y ^{2}}{0.9989 8 ^{2}} = 1

9 x^{2} + 25 y^{2} + 90 x = 0

x^{2} + 2 y^{2} = 11

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

\frac{( x - 3 ) ^{2}}{4} + \frac{( y - 3 ) ^{2}}{16} = 1

What is 9x^2+4y^2-36x+8y+31=0 ?
The solution to 9x^2+4y^2-36x+8y+31=0 is Ellipse with (h,k)=(2,-1),a=1,b= 3/2