- Home
- Standard 11
- Mathematics
10-1.Circle and System of Circles
normal
બે વર્તૂળો $x^2 + y^2 = ax$ અને $x^2 + y^2 = c^2 (c > 0)$ એકબીજાને ક્યારે સ્પર્શેં ?
A
$a = 2c$
B
$|a| = 2c$
C
$2 |a| = c$
D
$|a| = c$
Solution
The 2 circle $x^2+y^2=a x , x^2+y^2=c^2(c > 0)$ touch if:
$1^{\text {st }}$ circle:
$x^2+y^2=a x$
The centre lie at $c _1:\left(\frac{- a }{2}, 0\right)$ radius $r _1=\left|\frac{ a }{2}\right|$
$2^{\text {nd }}$ circle: $x^2+y^2=c^2$
$c _2=(0,0), r _2= c$
$2$ circle touch each other if:
$\left|c_1 c_2\right|=r_1 \pm r_2$
$\therefore\left|\left(-\frac{a}{2}\right)^2\right|=\left(\pm \frac{a}{2} \pm c\right)^2$
$\frac{a^2}{4}=\frac{a^2}{4}+c^2 \pm|a| c$
$|a| c=c^2$
$|a|=c$
Standard 11
Mathematics
