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Beliebt Geometry >

(3p+2q)2=9p^2+4q^2

Lösung

(3 p + 2 q) 2 = 9 p^{2} + 4 q^{2}

Lösung

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

Schritte zur Lösung

(3 p + 2 q) \cdot 2 = 9 p^{2} + 4 q^{2}

Rewrite

(3 p + 2 q) 2 - 9 p^{2} - 4 q^{2} = 0

in the form of the standard ellipse equation

\frac{( p - \frac{1}{3} ) ^{2}}{( \frac{2}{3} ) ^{2}} + \frac{( q - \frac{1}{2} ) ^{2}}{( \frac{1}{2} ) ^{2}} = 1

Therefore ellipse properties are:

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

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

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

Graph

Beliebte Beispiele

((x-5)^2)/9+((y-4)^2)/(36)=1

\frac{( x - 5 ) ^{2}}{9} + \frac{( y - 4 ) ^{2}}{36} = 1

(x^2)/4+(y^2)/(20)=1

\frac{x ^{2}}{4} + \frac{y ^{2}}{20} = 1

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

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

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

(x^2)/9+(y^2)/(20)=1

\frac{x ^{2}}{9} + \frac{y ^{2}}{20} = 1