What is 9x^2+4y^2-18x+8y=23 ?

The solution to 9x^2+4y^2-18x+8y=23 is Ellipse with (h,k)=(1,-1),a=2,b=3

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9x^2+4y^2-18x+8y=23

9 x^{2} + 4 y^{2} - 18 x + 8 y = 23

(h, k) = (1, - 1), a = 2, b = 3

Solution steps

9 x^{2} + 4 y^{2} - 18 x + 8 y = 23

Rewrite

9 x^{2} + 4 y^{2} - 18 x + 8 y = 23

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

(h, k) = (1, - 1), a = 2, b = 3

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (1, - 1), b = 3, a = 2

1 x^{2} + 2 y^{2} = 9

\frac{( x - 3 ) ^{2}}{64} + \frac{( y - 3 ) ^{2}}{16} = 1

4 x^{2} + y^{2} + 48 x + 128 = 0

\frac{( x - 2 ) ^{2}}{9} + \frac{( y + 4 ) ^{2}}{16} = 1

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

What is 9x^2+4y^2-18x+8y=23 ?
The solution to 9x^2+4y^2-18x+8y=23 is Ellipse with (h,k)=(1,-1),a=2,b=3