JEE Mains · Maths · STD 11 - 10.1 circle and system of circle
Four distinct points \((2 \mathrm{k}, 3 \mathrm{k}),(1,0),(0,1)\) and \((0,0)\) lie on a circle for \(k\) equal to :
- A \(\frac{2}{13}\)
- B \(\frac{3}{13}\)
- C \(\frac{5}{13}\)
- D \(\frac{1}{13}\)
Answer & Solution
Correct Answer
(C) \(\frac{5}{13}\)
Step-by-step Solution
Detailed explanation
\((2 \mathrm{k}, 3 \mathrm{k})\) will lie on circle whose diameter is \(\mathrm{AB} \).. \( (x-1)(x)+(y-1)(y)=0 \) \( x^2+y^2-x-y=0\) \(........(i)\) Satisfy \((2k, 3k)\) in \((i)\) \((2 \mathrm{k})^2+(3 \mathrm{k})^2-2 \mathrm{k}-3 \mathrm{k}=0\)…
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