TS EAMCET · Maths · Circle
If the radical centre of the given three circles \(x^2+y^2=1, x^2+y^2-2 x-3=0\) and \(x^2+y^2-2 y-3=0\) is \(C(\alpha, \beta)\) and \(r\) is the sum of the radii of the given circles, then the circle with \(C(\alpha, \beta)\) as centre and r as radius is
- A \((x-1)^2+(y-1)^2=2\)
- B \((x-1)^2+(y+1)^2=4\)
- C \((x-2)^2+(y-2)^2=25\)
- D \((x+1)^2+(y+1)^2=25\)
Answer & Solution
Correct Answer
(D) \((x+1)^2+(y+1)^2=25\)
Step-by-step Solution
Detailed explanation
\(\mathrm{S}_1: x^2+y^2-1=0 ; \mathrm{S}_2: x^2+y^2-2 x-3=0\) \(\mathrm{S}_3: x^2+y^2-2 y-3=0\) \(S_1-S_2=0\)(Equation of radical axis) \[ \begin{aligned} & 2 x+2=0 \\ & x=-1 \\ & \mathrm{~S}_1-\mathrm{S}_3=0 \\ & 2 y+2=0 \\ & y=-1 \end{aligned} \] \(\therefore\) Radical centre…
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