A) \[\left( \frac{2}{5},\frac{1}{5} \right)or\left( -\frac{2}{5},-\frac{1}{5} \right)\]
B) \[\left( -\frac{2}{5},\frac{1}{5} \right)or\left( \frac{2}{5},-\frac{1}{5} \right)\]
C) \[\left( -\frac{2}{5},-\frac{1}{5} \right)\]
D) \[\left( -\frac{3}{5},-\frac{2}{5} \right)or\left( \frac{3}{5},\frac{2}{5} \right)\]
E) \[\left( -\frac{3}{5},\frac{2}{5} \right)or\left( \frac{3}{5},-\frac{2}{5} \right)\]
Correct Answer: B
Solution :
We have, \[{{a}^{2}}=\frac{1}{4},{{b}^{2}}=\frac{1}{9},m=\frac{8}{9}\] The required points are \[\left( \pm \frac{{{a}^{2}}m}{\sqrt{{{a}^{2}}{{m}^{2}}+{{b}^{2}}}},\mp \frac{{{b}^{2}}}{\sqrt{{{a}^{2}}{{m}^{2}}+{{b}^{2}}}} \right)\] \[\left( \pm \frac{\frac{1}{4}.\frac{8}{9}}{\sqrt{\frac{1}{4}\times \frac{64}{84}+\frac{1}{9}}},\mp \frac{\frac{1}{9}}{\sqrt{\frac{1}{4}\times \frac{64}{81}+\frac{1}{9}}} \right)\] i.e., \[\left( \pm \frac{2}{5}\mp \frac{1}{5} \right)\]
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