(x^2}{25}+\frac{y^2)/9 <1

Lösung

\frac{x ^{2}}{25} + \frac{y ^{2}}{9} < 1

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

Schritte zur Lösung

\frac{x ^{2}}{25} + \frac{y ^{2}}{9} < 1

Rewrite

\frac{x ^{2}}{25} + \frac{y ^{2}}{9} < 1

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

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

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

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

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

\frac{x ^{2}}{9} + \frac{y ^{2}}{\frac{9}{25}} = 1

y = 4 - \frac{x ^{2}}{4 y}

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

x^{2} + 4 y^{2} + 10 x + 8 y - 13 = 0