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

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

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

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

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

Solution steps

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

Rewrite

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

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

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

x^{2}

y^{2} = - 12 x

9 x^{2} - y^{2} - 36 x - 6 y + 18 = 0

9 y^{2} - 16 x^{2} = 144

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