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AP EAMCET · Maths · Straight Lines

Let the curve \(x^2+2 y^2=2\) intersect the line \(x+y=1\) at two points \(\mathrm{P}\) and \(\mathrm{Q}\) and \(\mathrm{O}\) be the origin. If \(\theta\) is the acute angle between the lines \(\mathrm{OP}\) and \(\mathrm{OQ}\), then \(\tan \theta=\)

  1. A \(\frac{1}{4}\)
  2. B \(4\)
  3. C \(\sqrt{3}\)
  4. D \(\frac{1}{\sqrt{3}}\)
Verified Solution

Answer & Solution

Correct Answer

(B) \(4\)

Step-by-step Solution

Detailed explanation

Given the curve \(x^2+2 y^2=2 \& x+y=1\) \(\begin{aligned} & x^2+2 y^2=2 \Rightarrow x^2+2 y^2=2(1)^2 \\ & \Rightarrow x^2+2 y^2=2(x+y)^2 \\ & \Rightarrow x^2+2 y^2=2 x^2+2 y^2+4 x y \Rightarrow x^2+4 x y=0 \end{aligned}\) Now,…