Discussion
Coordinates of a point (x, y) on a circle having centre at \((x_{c}, y_{c})\) and polar coordinates r and θ may be expressed in parametric polar form as :
Answer: A
The parametric form is \(x = x_{c} + r\cos\theta,\ y = y_{c} + r\sin\theta\).
A point at distance r from the centre at angle \(\theta\) measured from the positive x-axis lies \(r\cos\theta\) to the right of the centre and \(r\sin\theta\) above it. Adding the centre's coordinates gives the point. As \(\theta\) runs from 0 to \(2\pi\), the point traces the whole circle.
Swapping sin and cos, as in (B), traces the same circle starting from the top and going the other way, which is not the standard polar form. Options (C) and (D) give x and y the same function of \(\theta\), so they trace a straight diagonal segment, not a circle.
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