A) \[\sqrt{{{a}^{2}}+{{p}^{2}}}+\sqrt{{{b}^{2}}+{{p}^{2}}}\]
B) \[\sqrt{{{a}^{2}}-{{p}^{2}}}+\sqrt{{{b}^{2}}-{{p}^{2}}}\]
C) \[\sqrt{{{a}^{2}}-{{p}^{2}}}-\sqrt{{{b}^{2}}-{{p}^{2}}}\]
D) \[\sqrt{{{a}^{2}}+{{p}^{2}}}-\sqrt{{{b}^{2}}+{{p}^{2}}}\]
Correct Answer: C
Solution :
[c] The given circles are concentric with centre at (0, 0) and the length of the perpendicular from (0, 0) on the given line is p. Let OL = p Then, \[AL=\sqrt{O{{A}^{2}}-O{{L}^{2}}}=\sqrt{{{a}^{2}}-{{p}^{2}}}\] and \[PL=\sqrt{O{{P}^{2}}-O{{L}^{2}}}=\sqrt{{{b}^{2}}-{{p}^{2}}}\] \[\Rightarrow AP=\sqrt{{{a}^{2}}-{{p}^{2}}}-\sqrt{{{b}^{2}}-{{p}^{2}}}\]You need to login to perform this action.
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