TS EAMCET · Maths · Circle
The polar equation of the circle with centre \(\left(2, \frac{\pi}{2}\right)\) and radius 3 units is :
- A \(r^2+4 r \cos \theta=5\)
- B \(r^2+4 r \sin \theta=5\)
- C \(r^2-4 r \sin \theta=5\)
- D \(r^2-4 r \cos \theta=5\)
Answer & Solution
Correct Answer
(C) \(r^2-4 r \sin \theta=5\)
Step-by-step Solution
Detailed explanation
\(r^2 - 2rr_0 \cos(\theta - \theta_0) + r_0^2 - a^2 = 0\) \(r^2 - 2r(2) \cos\left(\theta - \frac{\pi}{2}\right) + (2)^2 - (3)^2 = 0\) \(r^2 - 4r \sin(\theta) + 4 - 9 = 0\) \(r^2 - 4r \sin(\theta) = 5\)
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