achse 4x^2+9y^2-8x+90y+193=0

Lösung

achse

4 x^{2} + 9 y^{2} - 8 x + 90 y + 193 = 0

semi - major axis a = 3, semi - minor axis b = 2

Schritte zur Lösung

4 x^{2} + 9 y^{2} - 8 x + 90 y + 193 = 0

Rewrite

4 x^{2} + 9 y^{2} - 8 x + 90 y + 193 = 0

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

(h, k) = (1, - 5), a = 3, b = 2

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (1, - 5), a = 3, b = 2

a x i s \frac{x ^{2}}{49} + \frac{y ^{2}}{169} = 1

a x i s 5 x^{2} + 7 y^{2} = 35

a x i s x^{2} + \frac{( y - 6 ) ^{2}}{16} = 1

a x i s \frac{( x + 2 ) ^{2}}{64} + \frac{( y - 1 ) ^{2}}{81} = 1

a x i s (\frac{x - 3}{9})^{2} + (\frac{y + 1}{4})^{2} = 1