A) \[\left[ \frac{a}{b}(b\pm \sqrt{{{a}^{2}}+{{b}^{2}}}),\,0 \right]\]
B) \[\left[ \frac{b}{a}(b\pm \sqrt{{{a}^{2}}+{{b}^{2}}}),\,0 \right]\]
C) \[\left[ \frac{a}{b}(a\pm \sqrt{{{a}^{2}}+{{b}^{2}}}),\,0 \right]\]
D) None of these
Correct Answer: A
Solution :
Let the point be \[(h,0)\], then \[a=\pm \frac{bh+0-ab}{\sqrt{{{a}^{2}}+{{b}^{2}}}}\] Þ \[bh=\pm a\sqrt{{{a}^{2}}+{{b}^{2}}}+ab\Rightarrow h=\frac{a}{b}(b\pm \sqrt{{{a}^{2}}+{{b}^{2}}})\] Hence the point is \[\left\{ \frac{a}{b}(b\pm \sqrt{{{a}^{2}}+{{b}^{2}}}),0 \right\}\].
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