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Find the equations and length of major and minor axes of $9x^{2}+4y^{2}=20$

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Toolbox:
  • Standard forms of equation of the ellipse with major axes 2a, minor axis 2b $(a >b)$ eccentricity e and $b^2=a^2(1-e^2)$ or $e^2=1-\large\frac{b^2}{a^2}$
  • $\large\frac{x^2}{a^2}+\frac{y^2}{b^2}$$=1$
  • http://clay6.com/mpaimg/7_2_Toolbox.png
  • Foci$(\pm ae,o),$ center $(0,0)$,vertices $(\pm a,0)$
  • End points of Latus Rectum $ (ae,\pm \large\frac{b^2}{a})$ and $(-ae,\pm \large\frac{b^2}{a})$
  • Directrices $x=\pm \large\frac{a}{e}$.
  • The major axis is $y=0$ (x- axis) and the minor axes is $x=0$ (y- axis)
  • $\large\frac{x^2}{b^2}+\frac{y^2}{a^2}$$=1$
  • http://clay6.com/mpaimg/7_2_Toolbox1.png
  • Foci$(0,\pm ae),$ center $(0,0)$,vertices $(0,\pm a)$
  • End points of Latus Rectum $(\pm \large\frac{b^2}{a}$$,ae)$ and $(\pm \large\frac{b^2}{a}$$,-ae)$
  • Directrices $y=\pm \large\frac{a}{e}$.
  • The major axis is $x=0$ (y- axis) and the minor axes is $y=0$ (x- axis)
Step 1:
$9x^2+4y^2=20$
The above equation is dividing by $20$ we get
$\Large\frac{x^2}{\Large\frac{20}{9}}+\large\frac{y^2}{5}$$=1$
$a^2=5,b^2=\large\frac{20}{9}$
$\Rightarrow a=\sqrt 5,b=\large\frac{2\sqrt 5}{3}$
Step 2:
Length of major axis=$2a=2\sqrt 5$
Length of minor axis=$2b=\large\frac{4\sqrt 5}{3}$
Equation of major axis $x=0$
Equation of minor axis $y=0$
answered Jun 17, 2013 by sreemathi.v
 

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