((x+1)^2)/5+((y-3)^2)/9 =1

Lösung

\frac{( x + 1 ) ^{2}}{5} + \frac{( y - 3 ) ^{2}}{9} = 1

(h, k) = (- 1, 3), a = 5, b = 3

Schritte zur Lösung

\frac{( x + 1 ) ^{2}}{5} + \frac{( y - 3 ) ^{2}}{9} = 1

Rewrite

\frac{( x + 1 ) ^{2}}{5} + \frac{( y - 3 ) ^{2}}{9} = 1

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

(h, k) = (- 1, 3), a = 5, b = 3

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (- 1, 3), b = 3, a = 5

x^{2} + 2 y^{2} + 4 x - 8 y - 6 = 0

8 x^{2} + 2 y^{2} - 32 = 0

16 x^{2} + 25 y^{2} - 96 x - 250 y + 369 = 0

78 = 32 (x - \frac{3}{2})^{2} + 50 (y + 1)^{2}

x^{2} + 2 y^{2} - 3 x + 8 y - 1 = 0