Category : JEE Main & Advanced
The distance between two points \[P({{x}_{1}},{{y}_{1}})\] and \[Q({{x}_{2}},{{y}_{2}})\] is given by \[PQ=\sqrt{{{(PR)}^{2}}+{{(QR)}^{2}}}=\sqrt{{{({{x}_{2}}-{{x}_{1}})}^{2}}+{{({{y}_{2}}-{{y}_{1}})}^{2}}}\]
Distance between two points in polar co-ordinates :
Let O be the pole and OX be the initial line. Let P and Q be two given points whose polar co-ordinates are \[({{r}_{1}},{{\theta }_{1}})\] and \[({{r}_{2}},{{\theta }_{2}})\] respectively.
Then, \[{{(PQ)}^{2}}=r_{1}^{2}+r_{2}^{2}-2{{r}_{1}}{{r}_{2}}\cos ({{\theta }_{1}}-{{\theta }_{2}})\]
\[\therefore \] \[PQ=\sqrt{r_{1}^{2}+r_{2}^{2}-2{{r}_{1}}{{r}_{2}}\cos ({{\theta }_{1}}-{{\theta }_{2}})}\],
where \[{{\theta }_{1}}\] and \[{{\theta }_{2}}\] in radians.
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