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}}{9} + \frac{z ^{2}}{49} = 1

x^{2} + 2 x + 4 y^{2} - 16 y + 1 = 0

\frac{( x - 1 ) ^{2}}{0. 1 ^{2}} + \frac{( y - 1 ) ^{2}}{0. 5 ^{2}} = 1

x^{2} + 2 y^{2} + 5 x - 2 y - 1 = 0

\frac{( x ^{2} )}{16} + \frac{( y ^{2} )}{25} = 1

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