64y^2+300x+100x^2=-81+256y

Lösung

64 y^{2} + 300 x + 100 x^{2} = - 81 + 256 y

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

Schritte zur Lösung

64 y^{2} + 300 x + 100 x^{2} = - 81 + 256 y

Rewrite

64 y^{2} + 300 x + 100 x^{2} = - 81 + 256 y

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

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

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

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

x^{2} + y^{2} - 9 - 4 x^{2} - 9 y^{2} - 36 = 0

- 16 x^{2} - 9 y^{2} = 144

7 x^{2} + 3 y^{2} = 55

\frac{( x - 2 ) ^{2}}{6} + \frac{( y - 6 2 ) ^{2}}{8} = 1

x^{2} + 64 x + 9 y^{2} + 162 y + 949 = 0