x^2+y^2-25=(x+25)/7-y

Lösung

x^{2} + y^{2} - 25 = \frac{x + 25}{7} - y

(h, k) = (\frac{1}{14}, - \frac{1}{2}), a = \frac{5 113}{7 2}, b = \frac{5 113}{7 2}

Schritte zur Lösung

x^{2} + y^{2} - 25 = \frac{x + 25}{7} - y

Rewrite

x^{2} + y^{2} - 25 - \frac{x + 25}{7} + y = 0

in the form of the standard ellipse equation

\frac{( x - \frac{1}{14} ) ^{2}}{( \frac{5 113}{7 2} ) ^{2}} + \frac{( y - ( - \frac{1}{2} ) ) ^{2}}{( \frac{5 113}{7 2} ) ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (\frac{1}{14}, - \frac{1}{2}), a = \frac{5 113}{7 2}, b = \frac{5 113}{7 2}

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (\frac{1}{14}, - \frac{1}{2}), b = \frac{5 113}{7 2}, a = \frac{5 113}{7 2}

\frac{( x - 4 ) ^{2}}{9} + \frac{( y - 2 ) ^{2}}{25} = 1

\frac{x ^{2}}{1.58 7 ^{2}} + \frac{y ^{2}}{0.9 9 ^{2}} = 1

4 x^{2} + 9 y^{2} - 144 = 0

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

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