9x^2+49y^2+18x+294y-9=0

Lösung

9 x^{2} + 49 y^{2} + 18 x + 294 y - 9 = 0

(h, k) = (- 1, - 3), a = 51, b = \frac{3 51}{7}

Schritte zur Lösung

9 x^{2} + 49 y^{2} + 18 x + 294 y - 9 = 0

Rewrite

9 x^{2} + 49 y^{2} + 18 x + 294 y - 9 = 0

in the form of the standard ellipse equation

\frac{( x - ( - 1 ) ) ^{2}}{( 51 ) ^{2}} + \frac{( y - ( - 3 ) ) ^{2}}{( \frac{3 51}{7} ) ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (- 1, - 3), a = 51, b = \frac{3 51}{7}

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (- 1, - 3), a = 51, b = \frac{3 51}{7}

\frac{x ^{2}}{4 ^{2}} + \frac{y ^{2}}{7 ^{2}} = 1

3 = x^{2} + 4 y^{2}

\frac{x ^{2}}{2.4 8 ^{2}} + \frac{y ^{2}}{2.7 5 ^{2}} = 1

x^{2} + 4 y^{2} - 16 y - 1 = - 1

3 x^{2} + 5 y^{2} - 1 = 0