Discussion
The line \(y = x - 1\) can be expressed in polar coordinates \((r, \theta)\) as
Answer: D
The line is \(r(\cos\theta - \sin\theta) = 1\).
Substitute \(x = r\cos\theta\) and \(y = r\sin\theta\) into \(y = x - 1\):
\[ \begin{aligned} r\sin\theta &= r\cos\theta - 1 \\ r\cos\theta - r\sin\theta &= 1 \\ r(\cos\theta - \sin\theta) &= 1 \end{aligned} \]
The option with a plus sign is the line \(x + y = 1\), which has slope \(-1\), not \(+1\). The options \(r = \cos\theta\) and \(r = \sin\theta\) are circles through the origin (\(x^{2} + y^{2} = x\) and \(x^{2} + y^{2} = y\)), not straight lines.
No comment is present. Be the first to comment.
Loading…
Post your comment
Please log in or register to post a comment.
Examination Categories
- SSC Exams
- Banking Exams
- Teaching Exams
- Civil Services Exams
- Railways Exams
- Engineering Recruitment Exams
- Defence Exams
- State Government Exams
- Police Exams
- Insurance Exams
- Nursing Exams
- Other Government Exams
- NRA CET
- PG Entrance Exams
- Campus Placement
- MBA Entrance Exams
- CUET and UG Entrance
- Judiciary Exams
- Regulatory Body Exams
- Software Development