What is 9x^2+4y^2-18x+8y-23=0 ?

The solution to 9x^2+4y^2-18x+8y-23=0 is Ellipse with (h,k)=(1,-1),a=2,b=3

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9x^2+4y^2-18x+8y-23=0

9 x^{2} + 4 y^{2} - 18 x + 8 y - 23 = 0

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

Solution steps

9 x^{2} + 4 y^{2} - 18 x + 8 y - 23 = 0

Rewrite

9 x^{2} + 4 y^{2} - 18 x + 8 y - 23 = 0

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

25 x^{2} + 4 y^{2} = 100

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

\frac{x ^{2}}{9} + \frac{y ^{2}}{16} = 1

x^{2} - y^{2} = 25

x^{2} + y^{2} = 100

What is 9x^2+4y^2-18x+8y-23=0 ?
The solution to 9x^2+4y^2-18x+8y-23=0 is Ellipse with (h,k)=(1,-1),a=2,b=3