WBJEE · Maths · Straight Lines
The locus of points \((x, y)\) in the plane satisfying \(\sin ^2 x+\sin ^2 y=1\) consists of
- A a circle centered at origin
- B infinitely many circles that are all centered at the origin
- C infinitely many lines with slope \(\pm 1\)
- D finitely many lines with slope \(\pm 1\)
Answer & Solution
Correct Answer
(C) infinitely many lines with slope \(\pm 1\)
Step-by-step Solution
Detailed explanation
\(\begin{array}{r}\text {Hint: } \sin ^2 y=\cos ^2 x \\ \sin y= \pm \cos x \end{array}\) \(\begin{aligned} & \text { If } \sin y=\cos x=\sin \left(\frac{\pi}{2}-x\right) \\ & \Rightarrow y=n \pi+(-1)^n\left(\frac{\pi}{2}-x\right) \end{aligned}\)…
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