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Circle question

2024 · 8 Apr · Shift 1 · Q35
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  5. /2024 · 8 Apr · Shift 1 · Q35

Circle question

2024 · 8 Apr · Shift 1 · Q35

JEE MainMathematicsCircleMCQ+4 / −1
Let the circles C1:(x−α)2+(y−β)2=r12C_1:(x-\alpha)^2+(y-\beta)^2=r_1^2C1​:(x−α)2+(y−β)2=r12​ and C2:(x−8)2+(y−152)2=r22C_2:(x-8)^2+\left(y-\frac{15}{2}\right)^2=r_2^2C2​:(x−8)2+(y−215​)2=r22​ touch each other externally at the point (6,6)(6,6)(6,6). If the point (6,6)(6,6)(6,6) divides the line segment joining the centres of the circles C1C_1C1​ and C2C_2C2​ internally in the ratio 2:12: 12:1, then (α+β)+4(r12+r22)(\alpha+\beta)+4\left(r_1^2+r_2^2\right)(α+β)+4(r12​+r22​) equals
  1. A
    130
  2. B
    110
  3. C
    145
  4. D
    125
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