x^2+1/3 y^2=x+y

Lösung

x^{2} + \frac{1}{3} y^{2} = x + y

(h, k) = (\frac{1}{2}, \frac{3}{2}), a = 1, b = 3

Schritte zur Lösung

x^{2} + \frac{1}{3} y^{2} = x + y

Rewrite

x^{2} + \frac{1}{3} y^{2} = x + y

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

(h, k) = (\frac{1}{2}, \frac{3}{2}), a = 1, b = 3

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (\frac{1}{2}, \frac{3}{2}), b = 3, a = 1

36 x^{2} + 9 y^{2} + 48 x - 36 y + 43 = 0

4 x^{2} + 9 y^{2} - 48 x + 72 y + 144 = 0

4 x^{2} + 2 y^{2} + 2 x - 8 y + 7 = 0

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

\frac{( x - 6 ) ^{2}}{16} + \frac{( y + 3 ) ^{2}}{25} = 1