((y-2)^2)/4+((z-3)^2)/1 =1

Lösung

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

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

Schritte zur Lösung

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

Rewrite

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

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

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

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

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

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

a^{2} + 2 b^{2} = 1

- 25 x^{2} - 4 y^{2} + 100 = 4

\frac{( x - 6 ) ^{2}}{36} + \frac{( y + 2 ) ^{2}}{100} = 1

9 x^{2} - 72 x + 4 y^{2} + 40 y + 244 = 36