Q118 / 160 · TS EAMCET 2015 · Mathematics

The value of $a$, such that the power of the point $(1,6)$ with respect to the circle $x^2+y^2+4 x-6 y-a=0$, is -16 , is

  • A
    7
  • B
    11
  • C
    13
  • Correct answer
    D
    21

Solution

Given equation of the circle is $$ x^2+y^2+4 x-6 y-a=0 $$ We know that, power of point $P(1,6)$ w.r.t. the circle $$ \begin{array}{rrrr} & x^2+y^2+4 x-6 y-a \text { is }-16 \\ \therefore & 1+36+4-36-a=-16 \\ \Rightarrow & 5-a=-16 \\ \Rightarrow & a & =21 \end{array} $$

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

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