((x-2)^2)/(2/(sqrt(3)))+((y-1)^2)/(16)=1

Lösung

\frac{( x - 2 ) ^{2}}{\frac{2}{3}} + \frac{( y - 1 ) ^{2}}{16} = 1

(h, k) = (2, 1), a = \frac{2}{3}, b = 4

Schritte zur Lösung

\frac{( x - 2 ) ^{2}}{\frac{2}{3}} + \frac{( y - 1 ) ^{2}}{16} = 1

Rewrite

\frac{( x - 2 ) ^{2}}{\frac{2}{3}} + \frac{( y - 1 ) ^{2}}{16} = 1

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

(h, k) = (2, 1), a = \frac{2}{3}, b = 4

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (2, 1), b = 4, a = \frac{2}{3}

\frac{x ^{2}}{36} + \frac{y ^{2}}{121} = 1

(x + 8)^{2} + (\frac{y + 1}{2})^{2} = 3

4 x^{2} + y^{2} - 8 x + 6 y + 9 = 0

\frac{( x + 3 ) ^{2}}{24} + \frac{( y - 5 ) ^{2}}{49} = 1

\frac{( x + 3 ) ^{2}}{64} + \frac{( y - 6 ) ^{2}}{100} = 1