x^2+6x+9+y^2=28.09+(9x^2)/(16)

Lösung

x^{2} + 6 x + 9 + y^{2} = 28.09 + \frac{9 x ^{2}}{16}

(h, k) = (- \frac{48}{7}, 0), a = 9.52127 \dots, b = 6.29773 \dots

Schritte zur Lösung

x^{2} + 6 x + 9 + y^{2} = 28.09 + \frac{9 x ^{2}}{16}

Rewrite

x^{2} + 6 x + 9 + y^{2} - 28.09 - \frac{9 x ^{2}}{16} = 0

in the form of the standard ellipse equation

\frac{( x - ( - \frac{48}{7} ) ) ^{2}}{9.52127 \dots ^{2}} + \frac{( y - 0 ) ^{2}}{6.29773 \dots ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (- \frac{48}{7}, 0), a = 9.52127 \dots, b = 6.29773 \dots

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (- \frac{48}{7}, 0), a = 9.52127 \dots, b = 6.29773 \dots

\frac{( x + 2 ) ^{2}}{36} + \frac{( y - 3 ) ^{2}}{9} = 1

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

x^{2} + 4 y^{2} - 2 x + 16 y + 1 = 0

4 x^{2} + 2 y^{2} - 2 x + 4 y - 7 = 0

\frac{( x - 4 ) ^{2}}{36} + \frac{y ^{2}}{20} = 1