The product of the perpendiculars drawn from the foci of the ellipse , \frac{x^{2}}{9}+\frac{y^{2}}{25}=1   upon the tangent to it at the point
\left ( \frac{3}{2} ,\frac{5\sqrt{3}}{2}\right ),\; is:
  • Option 1)

    3\sqrt{3}\;

  • Option 2)

    9\;

  • Option 3)

    \frac{189}{13}\;

  • Option 4)

    18

 

Answers (1)

As learnt in

Foci of Ellipse -

The two fixed points on the ellipse.

- wherein

 

 Product of perpendicular drawn from foci is always = b2

In ellipse \frac{x^{2}}{9}+\frac{y^{2}}{25}=1;\frac{x^{2}}{9}+\frac{y^{2}}{25}=1;\:a^{2}=25,\:b^{2}=9

Hence product =9


Option 1)

3\sqrt{3}\;

This option is incorrect.

Option 2)

9\;

This option is correct.

Option 3)

\frac{189}{13}\;

This option is incorrect.

Option 4)

18

This option is incorrect.

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