((x-3)^2)/(25)+((y+1)^2)/(16)=1

Lösung

\frac{( x - 3 ) ^{2}}{25} + \frac{( y + 1 ) ^{2}}{16} = 1

(h, k) = (3, - 1), a = 5, b = 4

Schritte zur Lösung

\frac{( x - 3 ) ^{2}}{25} + \frac{( y + 1 ) ^{2}}{16} = 1

Rewrite

\frac{( x - 3 ) ^{2}}{25} + \frac{( y + 1 ) ^{2}}{16} = 1

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

(h, k) = (3, - 1), a = 5, b = 4

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (3, - 1), a = 5, b = 4

25 x^{2} + 16 y^{2} - 150 x + 128 y + 81 = 0

25 x^{2} + y^{2} - 100 x + 8 y + 91 = 0

49 x^{2} + 16 y^{2} = 784

\frac{( x - 6 ) ^{2}}{36} + \frac{( y + 1 ) ^{2}}{25} = 1

x^{2} + 4 y^{2} - 2 x - 16 y + 13 = 0