4x^2+9y^2-40x+36y+100=0

Lösung

4 x^{2} + 9 y^{2} - 40 x + 36 y + 100 = 0

(h, k) = (5, - 2), a = 3, b = 2

Schritte zur Lösung

4 x^{2} + 9 y^{2} - 40 x + 36 y + 100 = 0

Rewrite

4 x^{2} + 9 y^{2} - 40 x + 36 y + 100 = 0

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

(h, k) = (5, - 2), a = 3, b = 2

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (5, - 2), a = 3, b = 2

x^{2} + 3 y^{2} = 7

\frac{( x - 42 ) ^{2}}{12} + \frac{( y - 20 ) ^{2}}{27} = 1

16 x^{2} + 25 (y + 3)^{2} = 1600

\frac{( x - ( - 1.32 ) ) ^{2}}{3.78} + \frac{y ^{2}}{1.56} = 2

\frac{x ^{2}}{16} - \frac{x}{8} + 9 y^{2} - 18 y + \frac{17}{2} = 0