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10-1.Circle and System of Circles
hard
જો વક્રો $x^{2}-6 x+y^{2}+8=0$ અને $\mathrm{x}^{2}-8 \mathrm{y}+\mathrm{y}^{2}+16-\mathrm{k}=0,(\mathrm{k}>0)$ એકબીજાના એક બિંદુમાં સ્પર્શે છે તો $\mathrm{k}$ ની મહતમ કિમંત મેળવો.
A
$25$
B
$36$
C
$30$
D
$42$
(JEE MAIN-2020)
Solution
Common tangent is $\mathrm{S}_{1}-\mathrm{S}_{2}=0$
$\Rightarrow-6 x+8 y-8+k=0$
Use $\mathrm{p}=\mathrm{r}$ for $\mathrm{I}^{\text {st }}$ circle
$\Rightarrow \frac{|-18-8+k|}{10}=1$
$\Rightarrow \mathrm{k}=36$ or $16 \Rightarrow \mathrm{k}_{\max }=36$
Standard 11
Mathematics
