achse 4x^2+9y^2-8x-36y+4=0

Lösung

achse

4 x^{2} + 9 y^{2} - 8 x - 36 y + 4 = 0

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

Schritte zur Lösung

4 x^{2} + 9 y^{2} - 8 x - 36 y + 4 = 0

Rewrite

4 x^{2} + 9 y^{2} - 8 x - 36 y + 4 = 0

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

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

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

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

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

a x i s 3 x^{2} + 4 y^{2} + 27 x - 16 y + 48 = 0

a x i s x^{2} + y^{2} + 10 x - 8 y = - 32

a x i s \frac{( x + 5 ) ^{2}}{9} + \frac{( y + 1 ) ^{2}}{4} = 1

a x i s 2 x^{2} + 3 y^{2} = 4