Q59 / 160 · AP EAMCET 2010 · Mathematics

The equation of the radical axis of the pair of circles $7 x^2+7 y^2-7 x+14 y+18=0$ and $4 x^2+4 y^2-7 x+8 y+20=0$ is

  • A
    $x-2 y-5=0$
  • B
    $2 x-y+5=0$
  • Correct answer
    C
    $21 x-68=0$
  • D
    $23 x-68=0$

Solution

Let $S_1 \equiv x^2+y^2-x+2 y+\frac{18}{7}=0$ and $S_2 \equiv x^2+y^2-\frac{7}{4} x+2 y+5=0$ Now, the radical axis of the pair of circles are $S_1-S_2=0$ $\Rightarrow \quad\left(x^2+y^2-x+2 y+\frac{18}{7}\right)$ $-\left(x^2+y^2-\frac{7}{4} x+2 y+5\right)=0$ $\Rightarrow \quad-x+\frac{7}{4} x+\frac{18}{7}-5=0$ $\Rightarrow \quad-x+\frac{7}{4} x-\frac{17}{7}=0$ $\Rightarrow \quad-28 x+49 x-68=0$ $\Rightarrow \quad 21 x-68=0$

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

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