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Beliebt Geometry >

x^2+4y^2+9x+10y-14=0

Lösung

x^{2} + 4 y^{2} + 9 x + 10 y - 14 = 0

Lösung

(h, k) = (- \frac{9}{2}, - \frac{5}{4}), a = \frac{9}{2}, b = \frac{9}{2 2}

Schritte zur Lösung

x^{2} + 4 y^{2} + 9 x + 10 y - 14 = 0

Rewrite

x^{2} + 4 y^{2} + 9 x + 10 y - 14 = 0

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

(h, k) = (- \frac{9}{2}, - \frac{5}{4}), a = \frac{9}{2}, b = \frac{9}{2 2}

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (- \frac{9}{2}, - \frac{5}{4}), a = \frac{9}{2}, b = \frac{9}{2 2}

Graph

Beliebte Beispiele

((x+1)^2)/4+((y-3/2)^2)/8 =1

\frac{( x + 1 ) ^{2}}{4} + \frac{( y - \frac{3}{2} ) ^{2}}{8} = 1

((x-2)^2)/(4^2)+((y-3)^2)/(5^2)=1

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

25x^2+9y^2-25=0

25 x^{2} + 9 y^{2} - 25 = 0

y^2+5/2 y+(x^2)/4-44=0

y^{2} + \frac{5}{2} y + \frac{x ^{2}}{4} - 44 = 0

((x-14)^2)/3+((y-11)^2)/4 =1

\frac{( x - 14 ) ^{2}}{3} + \frac{( y - 11 ) ^{2}}{4} = 1