achse 4x^2-16x+25y^2+200y=-316

Lösung

achse

4 x^{2} - 16 x + 25 y^{2} + 200 y = - 316

semi - major axis a = 5, semi - minor axis b = 2

Schritte zur Lösung

4 x^{2} - 16 x + 25 y^{2} + 200 y = - 316

Rewrite

4 x^{2} - 16 x + 25 y^{2} + 200 y = - 316

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

(h, k) = (2, - 4), a = 5, b = 2

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (2, - 4), a = 5, b = 2

a x i s 3 x^{(2)} + 2 y^{(2)} - 12 x + 8 y + 19 = 0

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

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

a x i s 3 x^{2} + 3 y^{2} - 18 y = 0

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