question_answer

If \[A=[(x,\,y):{{x}^{2}}+{{y}^{2}}=25]\] and B = \[[(x,\,y):{{x}^{2}}+9{{y}^{2}}=144]\], then \[A\cap B\] contains [AMU 1996; Pb. CET 2002]

A) One point

B) Three points

C) Two points

D) Four points

Correct Answer: D

Solution :

A = Set of all values (x, y) : \[{{x}^{2}}+{{y}^{2}}=25={{5}^{2}}\] B = \[\frac{{{x}^{2}}}{144}+\frac{{{y}^{2}}}{16}=1\] i.e., \[\frac{{{x}^{2}}}{{{(12)}^{2}}}\] + \[\frac{{{y}^{2}}}{{{(4)}^{2}}}=1\]. Clearly, A Ç B consists of four points.