MHT CET · Maths · Straight Lines
If the polar co-ordinates of a point are \(\left(2, \frac{\pi^c}{4}\right)\), then its Cartesian co-ordinates are
- A \((\sqrt{2}, \sqrt{2})\)
- B (2,2)
- C \((2, \sqrt{2})\)
- D \((\sqrt{2}, 2)\)
Answer & Solution
Correct Answer
(A) \((\sqrt{2}, \sqrt{2})\)
Step-by-step Solution
Detailed explanation
Let the Cartesian coordinates by \((\mathrm{x}, \mathrm{y})\)
We have \(\sqrt{x^2+y^2}=2 \Rightarrow x^2+y^2=4\) and \(\tan \frac{\pi}{4}=\frac{y}{x} \Rightarrow 1=\frac{y}{x} \Rightarrow x=y\)
\(\therefore 2 x^2=4 \Rightarrow x^2=2 \Rightarrow x= \pm \sqrt{2} \Rightarrow y= \pm \sqrt{2}\)
We have \(\sqrt{x^2+y^2}=2 \Rightarrow x^2+y^2=4\) and \(\tan \frac{\pi}{4}=\frac{y}{x} \Rightarrow 1=\frac{y}{x} \Rightarrow x=y\)
\(\therefore 2 x^2=4 \Rightarrow x^2=2 \Rightarrow x= \pm \sqrt{2} \Rightarrow y= \pm \sqrt{2}\)
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