TS EAMCET · Maths · Circle
If the circles \(x^2+y^2-16 x-20 y+164=r^2(\mathrm{r}>0)\) and \(x^2+y^2-8 x-14 y+29=0\) intersect in two distinct points, then the maximum possible integral value of \(r\) is
- A 1
- B 10
- C -2
- D 2
Answer & Solution
Correct Answer
(B) 10
Step-by-step Solution
Detailed explanation
We have circles \[ \mathrm{S}_1 \equiv \mathrm{x}^2+\mathrm{y}^2-16 \mathrm{x}-20 \mathrm{y}+164-\mathrm{r}^2=0 \] and \(\mathrm{S}_2 \equiv \mathrm{x}^2+\mathrm{y}^2-8 \mathrm{x}-14 \mathrm{y}+29=0\) Here \(\mathrm{C}_1 \equiv(8,10)\) and \(\mathrm{C}_2 \equiv(4,7)\) Now…
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