TS EAMCET · Maths · Circle
\(\left(0, \frac{3}{4}\right)\) is the radical centre of the circles \(\begin{aligned} & S_1: x^2+y^2-2 x+6 y=0, \ & S_2: x^2+y^2+2 g x-2 y+6=0 \text { and } \ & S_3: x^2+y^2-12 x+2 f y+3=0 . \text { If } S_2 \text { and } S_3 \end{aligned}\) intersect orthogonally, then \((g, f)=\)
- A \(\left(\frac{-11}{12}, 1\right)\)
- B \(\left(1, \frac{-21}{2}\right)\)
- C \(\left(0, \frac{-9}{2}\right)\)
- D \(\left(-1, \frac{-7}{12}\right)\)
Answer & Solution
Correct Answer
(A) \(\left(\frac{-11}{12}, 1\right)\)
Step-by-step Solution
Detailed explanation
Radical axis of circle of \(\begin{aligned} & S_1=x^2+y^2-2 x+6 y=0 \\ & S_2=x^2+y^2+2 g x-2 y+6=0, \\ & S_3=x^2+y^2-12 x+2 f y+3=0 \text { is } S_2-S_3=0 \\ & \therefore(2 g+12) x-(2+2 f) y+6-3=0 \\ & (2 g+12) x-(2+2 f) y+3=0 \end{aligned}\) \(\left(0, \frac{3}{4}\right)\) is…
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