((x-0.5)^2}{10}+\frac{(y-3)^2)/5 =1

Lösung

\frac{( x - 0.5 ) ^{2}}{10} + \frac{( y - 3 ) ^{2}}{5} = 1

(h, k) = (0.5, 3), a = 10, b = 5

Schritte zur Lösung

\frac{( x - 0.5 ) ^{2}}{10} + \frac{( y - 3 ) ^{2}}{5} = 1

Rewrite

\frac{( x - 0.5 ) ^{2}}{10} + \frac{( y - 3 ) ^{2}}{5} = 1

in the form of the standard ellipse equation

\frac{( x - 0.5 ) ^{2}}{( 10 ) ^{2}} + \frac{( y - 3 ) ^{2}}{( 5 ) ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (0.5, 3), a = 10, b = 5

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (0.5, 3), a = 10, b = 5

x^{2} + 2 y^{2} < 1

(3 x - 3)^{2} + (2 y - 4)^{2} = 43 + 9 + 16

x^{2} + y^{2} + 12 y = 0

9 x^{2} + 25 y^{2} + 108 x - 200 y + 4 = 0

9 x^{2} + 16 y^{2} + 18 x - 32 y - 119 = 0