((x-6)^2}{25}+\frac{(y-7)^2)/9 =1

Lösung

\frac{( x - 6 ) ^{2}}{25} + \frac{( y - 7 ) ^{2}}{9} = 1

(h, k) = (6, 7), a = 5, b = 3

Schritte zur Lösung

\frac{( x - 6 ) ^{2}}{25} + \frac{( y - 7 ) ^{2}}{9} = 1

Rewrite

\frac{( x - 6 ) ^{2}}{25} + \frac{( y - 7 ) ^{2}}{9} = 1

in the form of the standard ellipse equation

\frac{( x - 6 ) ^{2}}{5 ^{2}} + \frac{( y - 7 ) ^{2}}{3 ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (6, 7), a = 5, b = 3

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (6, 7), a = 5, b = 3

8 x^{2} + y^{2} - 32 x - 16 y = - 16

\frac{x ^{2}}{16} + \frac{y ^{2}}{48} = 1

\frac{( x - 2 ) ^{2}}{9} + \frac{( y - 3 ) ^{2}}{5} = 1

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

16 x^{2} + 9 y^{2} - 128 x - 90 y + 337 = 0