What is (x^2)/9+(y^2)/4 = x/6+y/3 ?

The solution to (x^2)/9+(y^2)/4 = x/6+y/3 is Ellipse with (h,k)=(3/4 , 2/3),a= 5/4 ,b= 5/6

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(x^2)/9+(y^2)/4 = x/6+y/3

\frac{x ^{2}}{9} + \frac{y ^{2}}{4} = \frac{x}{6} + \frac{y}{3}

(h, k) = (\frac{3}{4}, \frac{2}{3}), a = \frac{5}{4}, b = \frac{5}{6}

Solution steps

\frac{x ^{2}}{9} + \frac{y ^{2}}{4} = \frac{x}{6} + \frac{y}{3}

Rewrite

\frac{x ^{2}}{9} + \frac{y ^{2}}{4} = \frac{x}{6} + \frac{y}{3}

in the form of the standard ellipse equation

\frac{( x - \frac{3}{4} ) ^{2}}{( \frac{5}{4} ) ^{2}} + \frac{( y - \frac{2}{3} ) ^{2}}{( \frac{5}{6} ) ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (\frac{3}{4}, \frac{2}{3}), a = \frac{5}{4}, b = \frac{5}{6}

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (\frac{3}{4}, \frac{2}{3}), a = \frac{5}{4}, b = \frac{5}{6}

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

\frac{( x - 4 ) ^{2}}{4} + \frac{( y + 1 ) ^{2}}{9} = 1

\frac{( x - 1.29 ) ^{2}}{1.17} + \frac{y ^{2}}{2.77} = 2

(\frac{x}{9})^{2} + (\frac{y}{4})^{2} = 1

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

What is (x^2)/9+(y^2)/4 = x/6+y/3 ?
The solution to (x^2)/9+(y^2)/4 = x/6+y/3 is Ellipse with (h,k)=(3/4 , 2/3),a= 5/4 ,b= 5/6