A) \[{{a}^{2}}+{{b}^{2}}\]
B) \[a+b\]
C) \[{{a}^{2}}-{{b}^{2}}\]
D) \[\sqrt{{{a}^{2}}+{{b}^{2}}}\]
Correct Answer: D
Solution :
| [d] The distance between points |
| \[P(a\cos \theta +b\,\sin \theta ,0)\]and \[Q(0,\,\,\,a\sin \theta -b\,\cos \theta )\]is given by |
| \[PQ=\sqrt{{{(a\cos \theta +b\,\sin \theta -0)}^{2}}+{{(0-a\sin \theta +b\cos \theta )}^{2}}}\] |
| \[=\sqrt{\begin{align} & {{a}^{2}}{{\cos }^{2}}\theta +{{b}^{2}}{{\sin }^{2}}\theta +2ab\cos \theta \sin \theta +{{a}^{2}}{{\sin }^{2}}\theta \\ & +{{b}^{2}}{{\cos }^{2}}\theta -2ab\cos \theta \sin \theta \\ \end{align}}\] |
| \[=\sqrt{{{a}^{2}}({{\cos }^{2}}\theta +{{\sin }^{2}}\theta )+{{b}^{2}}({{\sin }^{2}}\theta +{{\cos }^{2}}\theta )}=\sqrt{{{a}^{2}}+{{b}^{2}}}\] |
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