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

Lösung

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

(h, k) = (0, 0), a = 15, b = \frac{3 5}{2 2}

Schritte zur Lösung

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

Rewrite

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

in the form of the standard ellipse equation

\frac{( x - 0 ) ^{2}}{( 15 ) ^{2}} + \frac{( y - 0 ) ^{2}}{( \frac{3 5}{2 2} ) ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (0, 0), a = 15, b = \frac{3 5}{2 2}

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (0, 0), a = 15, b = \frac{3 5}{2 2}

- 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

\frac{( x + 3 ) ^{2}}{21} + \frac{( y - 6 ) ^{2}}{25} = 1