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  • The focal distances of the point <img alt="\left ( 4\sqrt{3},5 \right )" src="https:/

The focal distances of the point \left ( 4\sqrt{3},5 \right )on the ellipse 25x^{2}+16y^{2}=1600 may be

Option: 1

7


Option: 2

6


Option: 3

12


Option: 4

11


Answers (1)

best_answer

As we learned

Ellipse -

Set of all points in plane, the sum of whose distances from two fixed points is constant.

- wherein

 

 

Ellipse\: is \: \frac{x^{2}}{64}+\frac{y^{2}}{100}= 1\Rightarrow a^{2}= 64,\\* b^{2}= 100\Rightarrow a^{2}=b^{2}\left ( 1-e^{2} \right )\left ( \because a<b \right )

\Rightarrow 64= 100\left ( 1-e^{2} \right )\Rightarrow e= \frac{3}{5}

Now focal distance of \left ( x_{1},y_{1} \right ) on ellipse \frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}=1\: \: \: \: \: \left ( a<b \right )

Must be b-ey_{1},b+ey_{1}  i.e. in this question they must be

10-\frac{3}{5}\times 5,10+\frac{3}{5}\times 5= 7\: and\: 13

Posted by

Ajit Kumar Dubey

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