Q49 / 90 · JEE Main 2011 · Mathematics

The two circles $x^2+y^2=a x$ and $x^2+y^2=c^2(c>0)$ touch each other if

  • Correct answer
    A
    $|a|=c$
  • B
    $a=2 c$
  • C
    $|a|=2 c$
  • D
    $2|a|=c$

Solution

$\mathrm{c}_1=\left(\frac{\mathrm{a}}{2}, 0\right) ; \mathrm{c}_2=(0,0)$ $\mathrm{r}_1=\frac{\mathrm{a}}{2} ; \mathrm{r}_2=\mathrm{c}$ $\mathrm{c}_1 \mathrm{c}_2=\mathrm{r}_1-\mathrm{r}_2 \Rightarrow \frac{\mathrm{a}}{2}=\mathrm{c}-\frac{\mathrm{a}}{2} \Rightarrow \mathrm{c}=\mathrm{a}$

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

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