AP EAMCET · Maths · Pair of Lines
If the lines given by \(\left(x^2+y^2\right) \sin ^2 \alpha=(x \cos \alpha-y \sin \alpha)^2\) are perpendicular to each other, then \(\sin ^2 \alpha+\tan ^2 \alpha=\)
- A \(\frac{15}{4}\)
- B 0
- C \(\frac{3}{2}\)
- D \(\frac{7}{12}\)
Answer & Solution
Correct Answer
(C) \(\frac{3}{2}\)
Step-by-step Solution
Detailed explanation
Given pair of lines \[ \begin{aligned} & \left(x^2+y^2\right) \sin ^2 \alpha=(x \cos \alpha-y \sin \alpha)^2 \\ & \Rightarrow x^2 \cos 2 \alpha+y^2(0)-2 x y \sin \alpha \cos \alpha=0 \end{aligned} \] Since lines are perpendicular.…
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