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Distance Formula

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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