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

x^{2} + 4 y^{2} - 4 x - 32 y + 32 = 0

\frac{( x - 1 ) ^{2}}{5} + \frac{( y + 2 ) ^{2}}{8} = 1

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

\frac{( x - 1 ) ^{2}}{9} + \frac{( y - 5 ) ^{2}}{25} = 1

\frac{x ^{2}}{6} + \frac{y ^{2}}{25} = 1

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