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Beliebt Geometry >

4x^2-2x+9y^2+6y=41

Lösung

4 x^{2} - 2 x + 9 y^{2} + 6 y = 41

Lösung

(h, k) = (\frac{1}{4}, - \frac{1}{3}), a = \frac{13}{4}, b = \frac{13}{6}

Schritte zur Lösung

4 x^{2} - 2 x + 9 y^{2} + 6 y = 41

Rewrite

4 x^{2} - 2 x + 9 y^{2} + 6 y = 41

in the form of the standard ellipse equation

\frac{( x - \frac{1}{4} ) ^{2}}{( \frac{13}{4} ) ^{2}} + \frac{( y - ( - \frac{1}{3} ) ) ^{2}}{( \frac{13}{6} ) ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (\frac{1}{4}, - \frac{1}{3}), a = \frac{13}{4}, b = \frac{13}{6}

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (\frac{1}{4}, - \frac{1}{3}), a = \frac{13}{4}, b = \frac{13}{6}

Graph

Beliebte Beispiele

((x-3)^2}{16}+(\frac{y+2)/9)^2=1

\frac{( x - 3 ) ^{2}}{16} + (\frac{y + 2}{9})^{2} = 1

9x^2+16y^2+18x-64y-71=0

9 x^{2} + 16 y^{2} + 18 x - 64 y - 71 = 0

((x-2.37)^2)/(2.85)+(y^2)/(4.14)=2

\frac{( x - 2.37 ) ^{2}}{2.85} + \frac{y ^{2}}{4.14} = 2

(x^2)/4+(y^2)/8 = 3/4

\frac{x ^{2}}{4} + \frac{y ^{2}}{8} = \frac{3}{4}

((x-5)^2)/9+((y-4)^2)/(25)=1

\frac{( x - 5 ) ^{2}}{9} + \frac{( y - 4 ) ^{2}}{25} = 1