4x^2+9y^2+16x+18y-11=0

Lösung

4 x^{2} + 9 y^{2} + 16 x + 18 y - 11 = 0

(h, k) = (- 2, - 1), a = 3, b = 2

Schritte zur Lösung

4 x^{2} + 9 y^{2} + 16 x + 18 y - 11 = 0

Rewrite

4 x^{2} + 9 y^{2} + 16 x + 18 y - 11 = 0

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

(h, k) = (- 2, - 1), a = 3, b = 2

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (- 2, - 1), a = 3, b = 2

\frac{( x + 3 ) ^{2}}{25} + \frac{( y - 1 ) ^{2}}{4} = 1

\frac{( x + 1 ) ^{2}}{16} + \frac{( y + 3 ) ^{2}}{9} = 1

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

\frac{( x + 2 ) ^{2}}{25} + \frac{( y - 5 ) ^{2}}{9} = 1

\frac{100}{1 + x ^{2} + 2 y ^{2}} = 1