18x^2+4y^2+4y-72x+37=0

Lösung

18 x^{2} + 4 y^{2} + 4 y - 72 x + 37 = 0

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

Schritte zur Lösung

18 x^{2} + 4 y^{2} + 4 y - 72 x + 37 = 0

Rewrite

18 x^{2} + 4 y^{2} + 4 y - 72 x + 37 = 0

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

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

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

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

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

25 x^{2} + 9 y^{2} - 150 x - 36 y = - 36

\frac{( x - 23 ) ^{2}}{841} + \frac{( y + 28 ) ^{2}}{484} = 1

3 x^{2} - 12 x + 2 y^{2} + 8 y + 14 = 0

(x - 7)^{2} + 6 y^{2} + 12 y = 0