((x-1)^2)/4+((y-5)^2)/(25)=1

Lösung

\frac{( x - 1 ) ^{2}}{4} + \frac{( y - 5 ) ^{2}}{25} = 1

(h, k) = (1, 5), a = 2, b = 5

Schritte zur Lösung

\frac{( x - 1 ) ^{2}}{4} + \frac{( y - 5 ) ^{2}}{25} = 1

Rewrite

\frac{( x - 1 ) ^{2}}{4} + \frac{( y - 5 ) ^{2}}{25} = 1

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

(h, k) = (1, 5), a = 2, b = 5

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (1, 5), b = 5, a = 2

16 x^{2} + 25 y^{2} - 128 x + 100 y = 0

\frac{( ( x + 0 ) ^{2} )}{40} + \frac{( ( y + 0 ) ^{2} )}{32} = 1

\frac{( x - 5 ) ^{2}}{16} + \frac{( y + 15 ) ^{2}}{25} = 1

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

36 x^{2} + 16 y^{2} = 576