x^2+4y^2+10x+8y-19=0

Lösung

x^{2} + 4 y^{2} + 10 x + 8 y - 19 = 0

(h, k) = (- 5, - 1), a = 43, b = 23

Schritte zur Lösung

x^{2} + 4 y^{2} + 10 x + 8 y - 19 = 0

Rewrite

x^{2} + 4 y^{2} + 10 x + 8 y - 19 = 0

in the form of the standard ellipse equation

\frac{( x - ( - 5 ) ) ^{2}}{( 4 3 ) ^{2}} + \frac{( y - ( - 1 ) ) ^{2}}{( 2 3 ) ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (- 5, - 1), a = 43, b = 23

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (- 5, - 1), a = 43, b = 23

- x^{2} - \frac{z ^{2}}{36} = 1

x^{2} + 36 y^{2} = 36

25 x^{2} + 16 y^{2} + 50 x + 64 y - 311 = 0

4 x^{2} - 24 x + 36 y^{2} - 360 y + 864 = 0

\frac{( x - 1 ) ^{2}}{64} + \frac{( y - 2 ) ^{2}}{25} = 1