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Beliebt Geometry >

2x^2+y^2-8y-2x+1=0

Lösung

2 x^{2} + y^{2} - 8 y - 2 x + 1 = 0

Lösung

(h, k) = (\frac{1}{2}, 4), a = \frac{31}{2}, b = \frac{31}{2}

Schritte zur Lösung

2 x^{2} + y^{2} - 8 y - 2 x + 1 = 0

Rewrite

2 x^{2} + y^{2} - 8 y - 2 x + 1 = 0

in the form of the standard ellipse equation

\frac{( x - \frac{1}{2} ) ^{2}}{( \frac{31}{2} ) ^{2}} + \frac{( y - 4 ) ^{2}}{( \frac{31}{2} ) ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (\frac{1}{2}, 4), a = \frac{31}{2}, b = \frac{31}{2}

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (\frac{1}{2}, 4), b = \frac{31}{2}, a = \frac{31}{2}

Graph

Beliebte Beispiele

8 x^{2} + 12 y^{2} = 96

(x^2)/9+(y^2)/4 = x/6+y/3

\frac{x ^{2}}{9} + \frac{y ^{2}}{4} = \frac{x}{6} + \frac{y}{3}

((x+1)^2}{36}+\frac{(y+2)^2)/9 =1

\frac{( x + 1 ) ^{2}}{36} + \frac{( y + 2 ) ^{2}}{9} = 1

((x-1.29)^2)/(1.17)+(y^2)/(2.77)=2

\frac{( x - 1.29 ) ^{2}}{1.17} + \frac{y ^{2}}{2.77} = 2

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

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