(x^2)/(1/2)+(y^2)/(1/2-16)=1

Lösung

\frac{x ^{2}}{\frac{1}{2}} + \frac{y ^{2}}{\frac{1}{2} - 16} = 1

(h, k) = (0, 0), a = \frac{1}{2}, b = i \frac{31}{2}

Schritte zur Lösung

\frac{x ^{2}}{\frac{1}{2}} + \frac{y ^{2}}{\frac{1}{2} - 16} = 1

Rewrite

\frac{x ^{2}}{\frac{1}{2}} + \frac{y ^{2}}{\frac{1}{2} - 16} = 1

in the form of the standard ellipse equation

\frac{( x - 0 ) ^{2}}{( \frac{1}{2} ) ^{2}} + \frac{( y - 0 ) ^{2}}{( i \frac{31}{2} ) ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (0, 0), a = \frac{1}{2}, b = i \frac{31}{2}

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (0, 0), a = \frac{1}{2}, b = i \frac{31}{2}

4 (x - 1)^{2} + 9 (y - 2)^{2} = 36

x^{2} + 8 y^{2} = 24

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

\frac{x ^{2}}{80} + \frac{y ^{2}}{12} = 1

36 x^{2} + 9 y^{2} = 324