Q53 / 160 · TS EAMCET 2014 · Mathematics

If tangents are drawn from any point on the circle $x^2+y^2=25$ to the ellipse $\frac{x^2}{16}+\frac{y^2}{9}=1$, then the angle between the tangents is

  • A
    $\frac{2 \pi}{3}$
  • B
    $\frac{pi}{4}$
  • C
    $\frac{pi}{3}$
  • Correct answer
    D
    $\frac{pi}{2}$

Solution

Given circle is a director circle to the given ellipse. $\therefore$ Angle between tangelt is $\theta=\frac{\pi}{2}$

Hence, the correct answer is option: 'D'.

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