An ellipse, with foci at (0,2) and (0, -2) and minor axis of length 4, passes through which of the following points?

 

 

  • Option 1)

    (\sqrt{2},2)

     

     

     

  • Option 2)

    (2,\sqrt{2})

  • Option 3)

    (2,2\sqrt{2})

  • Option 4)

    (1,2\sqrt{2})

 

Answers (1)

let   \frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}=1    (a<b)  is the equation of ellipse , focii (0,\pm 2)

Given : 2a = 4 => a = 2

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

4=b^{2}-4

8=b^{2}

\therefore equation of ellipse is

 \frac{x^{2}}{4}+\frac{y^{2}}{8}=1

=> it passes through (\sqrt2,2)

so, option 2 is correct.

 


Option 1)

(\sqrt{2},2)

 

 

 

Option 2)

(2,\sqrt{2})

Option 3)

(2,2\sqrt{2})

Option 4)

(1,2\sqrt{2})

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