Equation of the ellipse whose axes are the axes of coordinates and which passes through the point (–3, 1) and has eccentricity \sqrt{\frac{2}{5}}   is

  • Option 1)

    3x^{2}+5y^{2}-15=0\;

  • Option 2)

    \; 5x^{2}+3y^{2}-32=0\;

  • Option 3)

    \; 3x^{2}+5y^{2}-32=0\; \;

  • Option 4)

    \; 5x^{2}+3y^{2}-48=0

 

Answers (1)

As we learnt in 

Eccentricity -

e= \sqrt{1-\frac{b^{2}}{a^{2}}}

- wherein

For the ellipse  

\frac{x^{2}}{a^{2}}+ \frac {y^{2}}{b^{2}}= 1

 

 and

 

Standard equation -

\frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}= 1
 

- wherein

a\rightarrow Semi major axis

b\rightarrow Semi minor axis

 

 

Let equation of ellipse be  \frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}=1

It passes through (-3,1)

we get    \frac{9}{a^{2}}+\frac{1}{b^{2}}=1

Also, \: \frac{2}{5}=1-\frac{b^{2}}{a^{2}}

           \frac{b^{2}}{a^{2}}=\frac{3}{5}

On solving,  a^{2}=\frac{32}{3} \: \: ; \: \: b^{2}=\frac{33}{5}

We \ get, \: \: 3x^{2}+5y^{2}=32


Option 1)

3x^{2}+5y^{2}-15=0\;

This option is incorrect

Option 2)

\; 5x^{2}+3y^{2}-32=0\;

This option is incorrect

Option 3)

\; 3x^{2}+5y^{2}-32=0\; \;

This option is correct

Option 4)

\; 5x^{2}+3y^{2}-48=0

This option is incorrect

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