((x+3)^2)/4+(4y^2)/9 =1

Lösung

\frac{( x + 3 ) ^{2}}{4} + \frac{4 y ^{2}}{9} = 1

(h, k) = (- 3, 0), a = 2, b = \frac{3}{2}

Schritte zur Lösung

\frac{( x + 3 ) ^{2}}{4} + \frac{4 y ^{2}}{9} = 1

Rewrite

\frac{( x + 3 ) ^{2}}{4} + \frac{4 y ^{2}}{9} = 1

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

(h, k) = (- 3, 0), a = 2, b = \frac{3}{2}

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (- 3, 0), a = 2, b = \frac{3}{2}

9 (y^{2} + 6 y + 9) + 16 (x^{2} - 4 x + 4) = 81 + 64

\frac{( x - h ) ^{2}}{b ^{2}} + \frac{( y - k ) ^{2}}{a ^{2}} = 1

25 x^{(2)} + 9 y^{(2)} + 50 x - 108 y + 124 = 0

x^{2} + 2 z^{2} + 10 x - 16 z + 1 = 0

9 x^{2} + 4 y^{2} - 18 x + 24 y = 36