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Beliebt Geometry >

x^2+2y^2+5x-2y-1=0

Lösung

x^{2} + 2 y^{2} + 5 x - 2 y - 1 = 0

Lösung

(h, k) = (- \frac{5}{2}, \frac{1}{2}), a = \frac{31}{2}, b = \frac{31}{2 2}

Schritte zur Lösung

x^{2} + 2 y^{2} + 5 x - 2 y - 1 = 0

Rewrite

x^{2} + 2 y^{2} + 5 x - 2 y - 1 = 0

in the form of the standard ellipse equation

\frac{( x - ( - \frac{5}{2} ) ) ^{2}}{( \frac{31}{2} ) ^{2}} + \frac{( y - \frac{1}{2} ) ^{2}}{( \frac{31}{2 2} ) ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (- \frac{5}{2}, \frac{1}{2}), a = \frac{31}{2}, b = \frac{31}{2 2}

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (- \frac{5}{2}, \frac{1}{2}), a = \frac{31}{2}, b = \frac{31}{2 2}

Graph

Beliebte Beispiele

((x^2))/(16)+((y^2))/(25)=1

\frac{( x ^{2} )}{16} + \frac{( y ^{2} )}{25} = 1

((x^2)/9)+((y^2)/(16))=1

(\frac{x ^{2}}{9}) + (\frac{y ^{2}}{16}) = 1

16x^2+25y^2+160x+200y+400=0

16 x^{2} + 25 y^{2} + 160 x + 200 y + 400 = 0

36x^2+5y^2+216x-60y+324=0

36 x^{2} + 5 y^{2} + 216 x - 60 y + 324 = 0

x^2+4y^2+8x+9y-9=0

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