((x-1)^2)/(25)+((y+3)^2)/(100)=1

Lösung

\frac{( x - 1 ) ^{2}}{25} + \frac{( y + 3 ) ^{2}}{100} = 1

(h, k) = (1, - 3), a = 5, b = 10

Schritte zur Lösung

\frac{( x - 1 ) ^{2}}{25} + \frac{( y + 3 ) ^{2}}{100} = 1

Rewrite

\frac{( x - 1 ) ^{2}}{25} + \frac{( y + 3 ) ^{2}}{100} = 1

in the form of the standard ellipse equation

\frac{( x - 1 ) ^{2}}{5 ^{2}} + \frac{( y - ( - 3 ) ) ^{2}}{1 0 ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (1, - 3), a = 5, b = 10

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (1, - 3), b = 10, a = 5

\frac{x ^{2}}{1} + \frac{y ^{2}}{4} = 1

\frac{x ^{2}}{a ^{2}} + \frac{y ^{2}}{b ^{2}} \leq 1

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

3 x^{2} + 5 y^{2} = 15

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