100(x^2-x)+16(y^2-4y)=147

Lösung

100 (x^{2} - x) + 16 (y^{2} - 4 y) = 147

(h, k) = (\frac{1}{2}, 2), a = \frac{59}{5}, b = \frac{59}{2}

Schritte zur Lösung

100 (x^{2} - x) + 16 (y^{2} - 4 y) = 147

Rewrite

100 (x^{2} - x) + 16 (y^{2} - 4 y) = 147

in the form of the standard ellipse equation

\frac{( x - \frac{1}{2} ) ^{2}}{( \frac{59}{5} ) ^{2}} + \frac{( y - 2 ) ^{2}}{( \frac{59}{2} ) ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (\frac{1}{2}, 2), a = \frac{59}{5}, b = \frac{59}{2}

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (\frac{1}{2}, 2), b = \frac{59}{2}, a = \frac{59}{5}

14 x^{2} + 9 y^{2} = 126

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

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

5 x^{2} + 9 y^{2} - 10 x + 4 = 0

3 x^{(2)} + y^{(2)} - 24 x + 39 = 0