h(x)=6x^2-5x+7h(x)(2+h(x))

Lösung

h (x) = 6 x^{2} - 5 x + 7 h (x) (2 + h (x))

(h, k) = (\frac{5}{12}, - \frac{13}{14}), a = \frac{1189}{12 7}, b = \frac{1189}{14 6}

Schritte zur Lösung

y = 6 x^{2} - 5 x + 7 y (2 + y)

Rewrite

y - 6 x^{2} + 5 x - 7 y (2 + y) = 0

in the form of the standard ellipse equation

\frac{( x - \frac{5}{12} ) ^{2}}{( \frac{1189}{12 7} ) ^{2}} + \frac{( y - ( - \frac{13}{14} ) ) ^{2}}{( \frac{1189}{14 6} ) ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (\frac{5}{12}, - \frac{13}{14}), a = \frac{1189}{12 7}, b = \frac{1189}{14 6}

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (\frac{5}{12}, - \frac{13}{14}), a = \frac{1189}{12 7}, b = \frac{1189}{14 6}

0.8 x^{2} + y^{2} = 9

9 x^{2} + 36 x + y^{2} + 2 y + 36 = 0

25 x^{2} + 16 y^{2} + 200 x - 160 y + 400 = 0

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

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