x^2=2800^2+y^2-2(2800)(y)cos(20)

Lösung

x^{2} = 280 0^{2} + y^{2} - 2 (2800) (y) cos (2 0^{\circ})

(h, k) = (0, 2800 cos (2 0^{\circ})), a = 7840000 - 7840000 cos^{2} (2 0^{\circ}), b = 7840000 - 7840000 cos^{2} (2 0^{\circ})

Schritte zur Lösung

x^{2} = 280 0^{2} + y^{2} - 2 \cdot 2800 y cos (2 0^{\circ})

Rewrite

x^{2} = 280 0^{2} + y^{2} - 22800 y cos (2 0^{\circ})

in the form of a standard hyperbola equation

\frac{( x - 0 ) ^{2}}{( 7840000 - 7840000 cos ^{2} ( 2 0 ^{\circ} ) ) ^{2}} - \frac{( y - 2800 cos ( 2 0 ^{\circ} ) ) ^{2}}{( 7840000 - 7840000 cos ^{2} ( 2 0 ^{\circ} ) ) ^{2}} = 1

Therefore Hyperbola properties are:

(h, k) = (0, 2800 cos (2 0^{\circ})), a = 7840000 - 7840000 cos^{2} (2 0^{\circ}), b = 7840000 - 7840000 cos^{2} (2 0^{\circ})

x^{2} - (y - 3960)^{2} = 396 0^{2}

10 x^{2} - 64 y^{2} - 140 x + 768 y - 2304 = 0

\frac{x ^{2}}{3} - \frac{y ^{2}}{9} = 1

9 x^{2} - 25 y^{2} = 49

4 x^{2} - 5 y^{2} + 20 = 0