TS EAMCET · Maths · Straight Lines
If \(p\) and \(q\) are the perpendicular distances from the origin to the straight lines \(x \sec \theta-y \operatorname{cosec} \theta=a \quad\) and \(x \cos \theta+y \sin \theta=a \cos 2 \theta\), then
- A \(4 p^2+q^2=a^2\)
- B \(p^2+q^2=a^2\)
- C \(p^2+2 q^2=a^2\)
- D \(4 p^2+q^2=2 a^2\)
Answer & Solution
Correct Answer
(A) \(4 p^2+q^2=a^2\)
Step-by-step Solution
Detailed explanation
Given equations of straight lines are \[ \begin{aligned} x \sec \theta-y \operatorname{cosec} \theta & =a \\ x \cos \theta+y \sin \theta & =a \cos 2 \theta \end{aligned} \] Also, \(p=\) Perpendicular distance from the origin to the line (i)…
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