JEE Mains · Maths · STD 11 - 9. straight line
Consider the lines \(\mathrm{x}(3 \lambda+1)+\mathrm{y}(7 \lambda+2)=17 \lambda+5\), \(\lambda\) being a parameter, all passing through a point P . One of these lines (say L) is farthest from the origin. If the distance of \(L\) from the point \((3,6)\) is \(d\), then the value of \(d^2\) is
- A \(20\)
- B \(30\)
- C \(10\)
- D \(15\)
Answer & Solution
Correct Answer
(A) \(20\)
Step-by-step Solution
Detailed explanation
\(\begin{aligned} & \mathrm{x}(3 \lambda+1)+\mathrm{y}(7 \lambda+2)=17 \lambda+5 \\ & (\mathrm{x}+2 \mathrm{y}-5)+\lambda(3 \mathrm{x}+7 \mathrm{y}-17)=0 \end{aligned}\) intersection of family of lines \(\mathrm{P}(1,2)\) Let \(\mathrm{Q}(3,6)\)…
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