AP EAMCET · Maths · Pair of Lines
If \(\mathrm{P}\) is the set of all real numbers \(\alpha\) such that the product of the lengths of perpendiculars from \((\alpha, 1)\) to the pair of straight lines \(3 x^2+7 x y+2 y^2=0\) is \(\frac{\sqrt{2}}{5}\) then the sum of the elements in \(\mathrm{P}\) is
- A \(-\frac{11}{3}\)
- B \(-\frac{14}{3}\)
- C \(\frac{11}{3}\)
- D \(\frac{14}{3}\)
Answer & Solution
Correct Answer
(B) \(-\frac{14}{3}\)
Step-by-step Solution
Detailed explanation
\(3 x^2+7 x y+2 y^2=0 \implies (3x+y)(x+2y)=0\) The lines are \(L_1: 3x+y=0\) and \(L_2: x+2y=0\). The perpendicular distance from \((\alpha, 1)\) to \(L_1\) is \(d_1 = \frac{|3\alpha+1|}{\sqrt{3^2+1^2}} = \frac{|3\alpha+1|}{\sqrt{10}}\). The perpendicular distance from…
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