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Beliebt Geometry >

y+x-3=3y^2+2x^2

Lösung

y + x - 3 = 3 y^{2} + 2 x^{2}

Lösung

(h, k) = (\frac{1}{4}, \frac{1}{6}), a = \frac{67}{4 3}, b = \frac{67}{6 2}

Schritte zur Lösung

y + x - 3 = 3 y^{2} + 2 x^{2}

Rewrite

y + x - 3 = 3 y^{2} + 2 x^{2}

in the form of the standard ellipse equation

\frac{( x - \frac{1}{4} ) ^{2}}{( \frac{67}{4 3} ) ^{2}} + \frac{( y - \frac{1}{6} ) ^{2}}{( \frac{67}{6 2} ) ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (\frac{1}{4}, \frac{1}{6}), a = \frac{67}{4 3}, b = \frac{67}{6 2}

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (\frac{1}{4}, \frac{1}{6}), a = \frac{67}{4 3}, b = \frac{67}{6 2}

Graph

Beliebte Beispiele

4(x-1)^2+y^2=36

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

25(x^2+4x+4)+36(y^2+2y+1)=770

25 (x^{2} + 4 x + 4) + 36 (y^{2} + 2 y + 1) = 770

(x^2)/(81)+(y^2)/(144)=1

\frac{x ^{2}}{81} + \frac{y ^{2}}{144} = 1

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

(1+y^2)/(1-x^2)=2

\frac{1 + y ^{2}}{1 - x ^{2}} = 2