((x+0)^2)/(225/25)+((y-1)^2)/(225/9)=1

Lösung

\frac{( x + 0 ) ^{2}}{\frac{225}{25}} + \frac{( y - 1 ) ^{2}}{\frac{225}{9}} = 1

(h, k) = (0, 1), a = 3, b = 5

Schritte zur Lösung

\frac{( x + 0 ) ^{2}}{\frac{225}{25}} + \frac{( y - 1 ) ^{2}}{\frac{225}{9}} = 1

Rewrite

\frac{( x + 0 ) ^{2}}{\frac{225}{25}} + \frac{( y - 1 ) ^{2}}{\frac{225}{9}} = 1

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

(h, k) = (0, 1), a = 3, b = 5

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (0, 1), b = 5, a = 3

9 x^{2} - 72 x + y^{2} + 10 y + 160 = 0

\frac{x ^{2}}{3} + \frac{y ^{2}}{6} = 1

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

\frac{( x ^{2} )}{9} + \frac{( y ^{2} )}{16} = 1

(\frac{x ^{2}}{64}) + (\frac{y ^{2}}{25}) = 1