achse 9x^2+16y^2+90x+32y+97=0

Lösung

achse

9 x^{2} + 16 y^{2} + 90 x + 32 y + 97 = 0

semi - major axis a = 4, semi - minor axis b = 3

Schritte zur Lösung

9 x^{2} + 16 y^{2} + 90 x + 32 y + 97 = 0

Rewrite

9 x^{2} + 16 y^{2} + 90 x + 32 y + 97 = 0

in the form of the standard ellipse equation

\frac{( x - ( - 5 ) ) ^{2}}{4 ^{2}} + \frac{( y - ( - 1 ) ) ^{2}}{3 ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (- 5, - 1), a = 4, b = 3

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (- 5, - 1), a = 4, b = 3

a x i s \frac{( x - 4 ) ^{2}}{4} + \frac{y ^{2}}{16} = 1

a x i s x^{2} + 4 y^{2} - 6 x + 12 y - 11 = 0

a x i s x^{2} + 2 y^{2} = 4

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

a x i s (\frac{x - 1}{25})^{2} + (\frac{y - 3}{16})^{2} = 1