144x^2+169y^2-288x+676y-33516=0

Lösung

144 x^{2} + 169 y^{2} - 288 x + 676 y - 33516 = 0

(h, k) = (1, - 2), a = \frac{2146}{3}, b = \frac{4 2146}{13}

Schritte zur Lösung

144 x^{2} + 169 y^{2} - 288 x + 676 y - 33516 = 0

Rewrite

144 x^{2} + 169 y^{2} - 288 x + 676 y - 33516 = 0

in the form of the standard ellipse equation

\frac{( x - 1 ) ^{2}}{( \frac{2146}{3} ) ^{2}} + \frac{( y - ( - 2 ) ) ^{2}}{( \frac{4 2146}{13} ) ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (1, - 2), a = \frac{2146}{3}, b = \frac{4 2146}{13}

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (1, - 2), a = \frac{2146}{3}, b = \frac{4 2146}{13}

25 x^{2} + 50 x + 4 y^{2} - 16 y = 59

3 x^{2} + 8 y^{2} + 12 x + 48 y + 60 = 1

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

25 x^{(2)} + 16 y^{(2)} = 400

\frac{( y - 1 ) ^{2}}{16} + \frac{( x + 3 ) ^{2}}{4} = 1