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

x^{2} + 3 y^{2} + 2 x - 12 y + 10 = 0

4 x^{2} + 8 y^{2} + 6 x + 10 y - 12 = 0

4 x^{2} + 9 y^{2} - 32 x - 36 y + 64 = 0

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

25 x^{2} + 16 y^{2} + 100 x - 96 y - 156 = 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