What is 4x^2+9y^2-16x+18y-11=0 ?

The solution to 4x^2+9y^2-16x+18y-11=0 is Ellipse with (h,k)=(2,-1),a=3,b=2

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4x^2+9y^2-16x+18y-11=0

4 x^{2} + 9 y^{2} - 16 x + 18 y - 11 = 0

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

Solution steps

4 x^{2} + 9 y^{2} - 16 x + 18 y - 11 = 0

Rewrite

4 x^{2} + 9 y^{2} - 16 x + 18 y - 11 = 0

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

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

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

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

3 x^{2} + y^{2} - 24 x + 39 = 0

9 x^{2} + 16 y^{2} - 54 x + 64 y + 1 = 0

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

\frac{( x - 2 ) ^{2}}{36} + \frac{( y + 5 ) ^{2}}{9} = 1

x^{2} + y^{2} + 8 y = 0

What is 4x^2+9y^2-16x+18y-11=0 ?
The solution to 4x^2+9y^2-16x+18y-11=0 is Ellipse with (h,k)=(2,-1),a=3,b=2