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Beliebt Geometry >

4x^2+9y^2-40x+54y+1+5=0

Lösung

4 x^{2} + 9 y^{2} - 40 x + 54 y + 1 + 5 = 0

Lösung

(h, k) = (5, - 3), a = \frac{5 7}{2}, b = \frac{5 7}{3}

Schritte zur Lösung

4 x^{2} + 9 y^{2} - 40 x + 54 y + 1 + 5 = 0

Rewrite

4 x^{2} + 9 y^{2} - 40 x + 54 y + 1 + 5 = 0

in the form of the standard ellipse equation

\frac{( x - 5 ) ^{2}}{( \frac{5 7}{2} ) ^{2}} + \frac{( y - ( - 3 ) ) ^{2}}{( \frac{5 7}{3} ) ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (5, - 3), a = \frac{5 7}{2}, b = \frac{5 7}{3}

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (5, - 3), a = \frac{5 7}{2}, b = \frac{5 7}{3}

Graph

Beliebte Beispiele

9x^2+4y^2-18x+16y-119=0

9 x^{2} + 4 y^{2} - 18 x + 16 y - 119 = 0

25x^2+9y^2-100x+18x-116=0

25 x^{2} + 9 y^{2} - 100 x + 18 x - 116 = 0

x^2+2x+4y^2-16y+1=0

x^{2} + 2 x + 4 y^{2} - 16 y + 1 = 0

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

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

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

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