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CSS Pure Mathematics QUESTION #4097
Question 1
The polar equation \(r=2\cos\theta\) is equivalent to which Cartesian equation?
  • \(x^2+y^2=4\)
  • \((x-1)^2+y^2=1\)✔️
  • \(x^2+(y-1)^2=1\)
  • \((x-2)^2+y^2=2\)
Correct Answer Explanation
Multiply both sides by \(r\): \(r^2=2r\cos\theta\). Since \(r^2=x^2+y^2\) and \(r\cos\theta=x\): \(x^2+y^2=2x\Rightarrow x^2-2x+y^2=0\Rightarrow(x-1)^2+y^2=1\). This is a circle with center \((1,0)\) and radius \(1\).