Question

# Consider the circles S1:x2+y2−12y+35=0 S2:x2+y2−4x−4y+4=0 S1:x2+y2−9x=0 Which of the following statements is correct?

A
The centres of these three circles form a right triangle.
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B
Point (4,1) lies outside S1 but inside S2 and S3.
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C
The length of the chord intercepted on the line y=x by S3 is 32.
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D
Equation of the tangent on circle S3=0 at the origin is y=0
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Solution

## The correct option is B The length of the chord intercepted on the line y=x by S3 is 3√2.C1(0,6), C2(2,2), C3(3,0) are centres of S1,S2,S3 respectively which are collinear on line 2x+y=6 For point (4,1) S1>0 and S2>0 and S3<0 ∴ Point (4,1) lies inside S3 and outside S1 and S2 p=∣∣∣3√2∣∣∣ Now, 2l=2√9−92=3√2 Tangent at (0,0) on S3=0 is x=0.

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