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If the curves, \mathrm{x^2-6 x+y^2+8=0} and \mathrm{x^2-8 y+y^2+16-k=0,(k>0)} touch each other at a point, then the largest value of k is _________.

Option: 1

36


Option: 2

26


Option: 3

56


Option: 4

46


Answers (1)

best_answer

Two circles touches each other if \mathrm{C_1 C_2=\left|r_1 \pm r_2\right|}

Here, C_1(3,0) and \mathrm{C_2(0,4)\, \, . So, \, \, C_1 C_2=5}

Also, \mathrm{r_1=\sqrt{9+0-8}=1\, \, and \, \, r_2=\sqrt{0+16-16+k}=\sqrt{k}}

\mathrm{\therefore \sqrt{k}+1=5\, \, or \, \, |\sqrt{k}-1|=5}

\mathrm{\Rightarrow k=16\, \, or \, \, k=36 \Rightarrow} Maximum value of k is 36 .

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seema garhwal

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