36x^2+9y^2+48x-36y-72=0

Lösung

36 x^{2} + 9 y^{2} + 48 x - 36 y - 72 = 0

(h, k) = (- \frac{2}{3}, 2), a = \frac{31}{3}, b = \frac{2 31}{3}

Schritte zur Lösung

36 x^{2} + 9 y^{2} + 48 x - 36 y - 72 = 0

Rewrite

36 x^{2} + 9 y^{2} + 48 x - 36 y - 72 = 0

in the form of the standard ellipse equation

\frac{( x - ( - \frac{2}{3} ) ) ^{2}}{( \frac{31}{3} ) ^{2}} + \frac{( y - 2 ) ^{2}}{( \frac{2 31}{3} ) ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (- \frac{2}{3}, 2), a = \frac{31}{3}, b = \frac{2 31}{3}

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (- \frac{2}{3}, 2), b = \frac{2 31}{3}, a = \frac{31}{3}

\frac{( x - 3 ) ^{2}}{( 18 )} + \frac{( y + 1 ) ^{2}}{12} = 1

4 x^{2} + 8 y^{2} - 16 \cdot + 32 y + 32 = 0

y^{2} = \frac{4 - x ^{2}}{5}

490 x^{(2)} + 10 y^{(2)} + 808 x - 556 y + 40 = 0

\frac{x ^{2}}{2.3 2 ^{2}} + \frac{y ^{2}}{2.8 2 ^{2}} = 1