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10.1 circle and system of circle — MATHS STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceMATHS10.1 circle and system of circle1 Mark
MCQ
Two circle ${x^2} + {y^2} = ax$ and ${x^2} + {y^2} = {c^2}$ touch each other if 
  • ✓
    $|a|=c$
  • B
    $a=2c$
  • C
    $|a|=2c$
  • D
    $2|a|=c$
✓

Answer

Correct option: A.
$|a|=c$
a
The centres and radii are

$\left(x-\frac{a}{2}\right)^{2}+y^{2}=\frac{a^{2}}{4}, \quad x^{2}+y^{2}=c^{2}$

Centre $\left(\frac{a}{2}, 0\right)$ and $(0,0)$ and radius $=\frac{a}{2}$ and $c$

$\sqrt{\left(\frac{a}{2}\right)^{2}+(0-0)}=|| \frac{a}{2}|\pm c|$

$ \Rightarrow\left|\frac{a}{2}\right|=|| \frac{a}{2}|\pm c|$

$\Rightarrow\left|\frac{a}{2}\right|=c-\left|\frac{a}{2}\right|, \quad \therefore|a|=c$

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