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JEE Main 2011
Exam
JEE Main
Year
2011
Subject
Mathematics
Chapter
Circle

JEE Main 2011 · Mathematics · Circle

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

The two circles x2+y2=axx^2+y^2=a x and x2+y2=c2(c>0)x^2+y^2=c^2(c>0) touch each other if

Options

  1. A∣a∣=c|a|=c
  2. Ba=2ca=2 c
  3. C∣a∣=2c|a|=2 c
  4. D2∣a∣=c2|a|=c

Correct answer

A. ∣a∣=c|a|=c

Step-by-step solution

c1=(a2,0);c2=(0,0)\mathrm{c}_1=\left(\frac{\mathrm{a}}{2}, 0\right) ; \mathrm{c}_2=(0,0) r1=a2;r2=c\mathrm{r}_1=\frac{\mathrm{a}}{2} ; \mathrm{r}_2=\mathrm{c} c1c2=r1−r2⇒a2=c−a2⇒c=a\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}
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