16x^2-64x+25y^2+150y+189=0

Lösung

16 x^{2} - 64 x + 25 y^{2} + 150 y + 189 = 0

(h, k) = (2, - 3), a = \frac{5}{2}, b = 2

Schritte zur Lösung

16 x^{2} - 64 x + 25 y^{2} + 150 y + 189 = 0

Rewrite

16 x^{2} - 64 x + 25 y^{2} + 150 y + 189 = 0

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

(h, k) = (2, - 3), a = \frac{5}{2}, b = 2

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (2, - 3), a = \frac{5}{2}, b = 2

2 x^{2} + 3 y^{2} = 12

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

\frac{( y - 6 ) ^{2}}{36} + \frac{( x + 3 ) ^{2}}{16} = 1

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

\frac{( x - 1 ) ^{2}}{5} + \frac{( y - 3 ) ^{2}}{4} = 1