25x^2+16y^2+150x-128y-1119=0

Lösung

25 x^{2} + 16 y^{2} + 150 x - 128 y - 1119 = 0

(h, k) = (- 3, 4), a = 8, b = 10

Schritte zur Lösung

25 x^{2} + 16 y^{2} + 150 x - 128 y - 1119 = 0

Rewrite

25 x^{2} + 16 y^{2} + 150 x - 128 y - 1119 = 0

in the form of the standard ellipse equation

\frac{( x - ( - 3 ) ) ^{2}}{8 ^{2}} + \frac{( y - 4 ) ^{2}}{1 0 ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (- 3, 4), a = 8, b = 10

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (- 3, 4), b = 10, a = 8

\frac{x ^{2}}{4} + \frac{y ^{2}}{49} = 1

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

x^{2} + 4 y^{2} - 4 x - 32 y + 32 = 0

\frac{( x - 1 ) ^{2}}{5} + \frac{( y + 2 ) ^{2}}{8} = 1

\frac{x ^{2}}{6} + \frac{y ^{2}}{25} = 1