2x^2+3y^2+4x=19

Lösung

2 x^{2} + 3 y^{2} + 4 x = 19

(h, k) = (- 1, 0), a = \frac{21}{2}, b = 7

Schritte zur Lösung

2 x^{2} + 3 y^{2} + 4 x = 19

Rewrite

2 x^{2} + 3 y^{2} + 4 x = 19

in the form of the standard ellipse equation

\frac{( x - ( - 1 ) ) ^{2}}{( \frac{21}{2} ) ^{2}} + \frac{( y - 0 ) ^{2}}{( 7 ) ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (- 1, 0), a = \frac{21}{2}, b = 7

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (- 1, 0), a = \frac{21}{2}, b = 7

x^{2} + 6 x + (5 y + 6)^{2} - 2 (5 y + 6) + 10 = 4

4 x^{2} + 3 y^{2} - 32 x - 18 y + 43 = 0

9 x^{2} + 4 y^{2} + 90 x + 8 y + 193 = 0

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

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