What is x^2+3y^2-3x-5y=0 ?

The solution to x^2+3y^2-3x-5y=0 is Ellipse with (h,k)=(3/2 , 5/6),a=sqrt(13/3),b=(sqrt(13))/3

Popular >

x^2+3y^2-3x-5y=0

x^{2} + 3 y^{2} - 3 x - 5 y = 0

(h, k) = (\frac{3}{2}, \frac{5}{6}), a = \frac{13}{3}, b = \frac{13}{3}

Solution steps

x^{2} + 3 y^{2} - 3 x - 5 y = 0

Rewrite

x^{2} + 3 y^{2} - 3 x - 5 y = 0

in the form of the standard ellipse equation

\frac{( x - \frac{3}{2} ) ^{2}}{( \frac{13}{3} ) ^{2}} + \frac{( y - \frac{5}{6} ) ^{2}}{( \frac{13}{3} ) ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (\frac{3}{2}, \frac{5}{6}), a = \frac{13}{3}, b = \frac{13}{3}

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (\frac{3}{2}, \frac{5}{6}), a = \frac{13}{3}, b = \frac{13}{3}

x^{2} - 2 x + 4 y^{2} - 24 y + 33 = 0

\frac{x ^{2}}{1} + \frac{y ^{2}}{5} = 1

4 x^{2} + y^{2} + 56 = 4 y - 56 x

\frac{( x - 3 ) ^{2}}{49} + \frac{( y + 6 ) ^{2}}{100} = 1

\frac{( x - ( - 2 ) ) ^{2}}{9} + \frac{( y - 3 ) ^{2}}{25} = 1

What is x^2+3y^2-3x-5y=0 ?
The solution to x^2+3y^2-3x-5y=0 is Ellipse with (h,k)=(3/2 , 5/6),a=sqrt(13/3),b=(sqrt(13))/3