AP EAMCET · Maths · Circle
If the circles \(\mathrm{S} \equiv x^2+y^2-14 x+6 y+33=0\) and \(\mathrm{S}^{\prime} \equiv x^2+\) \(y^2-a^2=0(a \in \mathrm{~N})\) have 4 common tangents then possible number of values of \(a\) is
- A \(13\)
- B \(5\)
- C \(14\)
- D \(2\)
Answer & Solution
Correct Answer
(D) \(2\)
Step-by-step Solution
Detailed explanation
Given, \(S \equiv(x-7)^2+(y+3)^2=5^2\) So \(C=(7,-3), r=5\) and \(S^{\prime} \equiv x^2+y^2=a^2 \Rightarrow C^{\prime}=(0,0), r^{\prime}=a\) Since, for 4 common tangent \(C C^{\prime}\gtr+r^{\prime}\)…
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