4x^2+32x+9y^2-18y+37=0

Lösung

4 x^{2} + 32 x + 9 y^{2} - 18 y + 37 = 0

(h, k) = (- 4, 1), a = 3, b = 2

Schritte zur Lösung

4 x^{2} + 32 x + 9 y^{2} - 18 y + 37 = 0

Rewrite

4 x^{2} + 32 x + 9 y^{2} - 18 y + 37 = 0

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

(h, k) = (- 4, 1), a = 3, b = 2

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (- 4, 1), a = 3, b = 2

9 (5.66 - 2) x^{2} + y^{2} = 36

\frac{( x - 4 ) ^{2}}{16} + \frac{( y + 2 ) ^{2}}{36} = 1

y = \frac{2 x - 4}{- 2 y + 4} x + 6

x^{2} + 4 y^{2} + 9 x + 10 y - 14 = 0

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