JEE Mains · Maths · STD 11 - 10.1 circle and system of circle
The locus of a point, which moves such that the sum of squares of its distances from the points \((0,0),(1,0),(0,1)(1,1)\) is \(18\) units, is a circle of diameter \(\mathrm{d}\). Then \(\mathrm{d}^{2}\) is equal to ...... .
- A \(16\)
- B \(4\)
- C \(216\)
- D \(6\)
Answer & Solution
Correct Answer
(A) \(16\)
Step-by-step Solution
Detailed explanation
Let \(\mathrm{P}(\mathrm{x}, \mathrm{y})\) \(x^{2}+y^{2}+x^{2}+(y-1)^{2}+(x-1)^{2}+y^{2}+(x-1)^{2}+(y-1)^{2}=18;\) \(\Rightarrow 4\left(x^{2}+y^{2}\right)-4 y-4 x=14\) \(\Rightarrow x^{2}+y^{2}-x-y-\frac{7}{2}=0\) \(d=2 \sqrt{\frac{1}{4}+\frac{1}{4}+\frac{7}{2}}\)…
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