AP EAMCET · Maths · Circle
The radical centre of the three circles \(x^2+y^2-1=0, x^2+y^2-8 x+15=0\) and \(x^2+y^2+10 y+24=0\) is
- A \(\left(2, \frac{-5}{2}\right)\)
- B \(\left(2, \frac{5}{2}\right)\)
- C \(\left(-2, \frac{5}{2}\right)\)
- D \(\left(-2, \frac{-5}{2}\right)\)
Answer & Solution
Correct Answer
(A) \(\left(2, \frac{-5}{2}\right)\)
Step-by-step Solution
Detailed explanation
Let \(S_1: x^2+y^2-1=0\) ...(i) \(S_2: x^2+y^2-8 x+15=0\) ...(ii) and \(S_3: x^2+y^2+10 y+24=0\) ...(iii) From Eqs. (i) and (ii), \(8 x-15=1\) \(\Rightarrow \quad x=2\) Now, from Eqs. (i) and (iii), \(-10 y-24=1\) \(\Rightarrow-10 y=25 \Rightarrow y=\frac{-5}{2}\) Hence, the…
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