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

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

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

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

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

Solution steps

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

Rewrite

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

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

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

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

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

\frac{16 x ^{2}}{144} + \frac{9 y ^{2}}{144} = 1

x^{2} + 3 y^{2} - 13 - y^{2} - 4 x = 0

2 x^{2} - 200 x + y^{2} + 4 y + 379 = 0

\frac{x ^{2}}{\frac{25}{4}} + \frac{y ^{2}}{4} = 1

9 x^{2} + 4 y^{2} - 90 x + 189 = 0

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