AP EAMCET · Maths · Circle
Which of the following equations gives a circle?
- A \(r=2 \sin \theta\)
- B \(r^2 \cos 2 \theta=1\)
- C \(r(4 \cos \theta+5 \sin \theta)=3\)
- D \(5=r(1+\sqrt{2} \cos \theta)\)
Answer & Solution
Correct Answer
(A) \(r=2 \sin \theta\)
Step-by-step Solution
Detailed explanation
Now, taking option (a) i.e. \(r=2 \sin \theta\) Let \(x=r \sin \theta, y=r \cos \theta\) \(\Rightarrow \quad r^2=2 r \sin \theta\) \(\Rightarrow \quad x^2+y^2=2 y \quad\left[\because x^2+y^2=r^2\right]\) This equation represents a circle.
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