x^2+5y^2+6x-40y-167=0

Lösung

x^{2} + 5 y^{2} + 6 x - 40 y - 167 = 0

(h, k) = (- 3, 4), a = 16, b = \frac{16}{5}

Schritte zur Lösung

x^{2} + 5 y^{2} + 6 x - 40 y - 167 = 0

Rewrite

x^{2} + 5 y^{2} + 6 x - 40 y - 167 = 0

in the form of the standard ellipse equation

\frac{( x - ( - 3 ) ) ^{2}}{1 6 ^{2}} + \frac{( y - 4 ) ^{2}}{( \frac{16}{5} ) ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (- 3, 4), a = 16, b = \frac{16}{5}

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (- 3, 4), a = 16, b = \frac{16}{5}

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

4 x^{2} + 9 y^{2} + 8 x - 36 y + 4 = 0

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

x^{2} - 2 x + \frac{y ^{2}}{4} - y = 14

2 x^{2} + y^{2} + 12 x - 2 y + 17 = 0