(x^2+y^2+8y-16)/(x^2+y^2+8y+16)=9

Lösung

\frac{x ^{2} + y ^{2} + 8 y - 16}{x ^{2} + y ^{2} + 8 y + 16} = 9

(h, k) = (0, - 4), a = 2, b = 2

Schritte zur Lösung

\frac{x ^{2} + y ^{2} + 8 y - 16}{x ^{2} + y ^{2} + 8 y + 16} = 9

Rewrite

\frac{x ^{2} + y ^{2} + 8 y - 16}{x ^{2} + y ^{2} + 8 y + 16} = 9

in the form of the standard ellipse equation

\frac{( x - 0 ) ^{2}}{2 ^{2}} + \frac{( y - ( - 4 ) ) ^{2}}{2 ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (0, - 4), a = 2, b = 2

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (0, - 4), b = 2, a = 2

2 x^{2} - 9 x + 4 y^{2} + 8 x = 16

20 x^{2} + 9 y^{2} = 225

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

\frac{( ( x + 5 ) ^{2} )}{10} + \frac{( ( y + 4 ) ^{2} )}{8} = 1

3 x^{2} + y^{2} = 25