MHT CET · Maths · Circle
If A \((3,-2,2), \mathrm{B}(2, \lambda+1,5)\) are the end points of the diameter of the circle and if
the point \((5,6,-1)\) lies on the circle, then \(\lambda=\)
- A 6
- B 8
- C 7
- D 5
Answer & Solution
Correct Answer
(B) 8
Step-by-step Solution
Detailed explanation
The angle subtended at the point \(\mathrm{P}\) in the semicircle APB is a right angle. AP \(\perp P B\)
Now direction ratios of AP are \((5-3,6+2,-1-2)\) i.e. \((2,8,-3)\)
Now direction ratios of PB are \((2-5, \lambda+1-6,5+1)\) i.e. \((-3, \lambda-5,6)\)
Since AP \(\perp P B\), we write
(2) \((-3)+8(\lambda-5)-3(6)=0 \Rightarrow-6+8 \lambda-40\) \(-18=0\) \(\Rightarrow \lambda=8\)
Now direction ratios of AP are \((5-3,6+2,-1-2)\) i.e. \((2,8,-3)\)
Now direction ratios of PB are \((2-5, \lambda+1-6,5+1)\) i.e. \((-3, \lambda-5,6)\)
Since AP \(\perp P B\), we write
(2) \((-3)+8(\lambda-5)-3(6)=0 \Rightarrow-6+8 \lambda-40\) \(-18=0\) \(\Rightarrow \lambda=8\)
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