A) \[(\pm a,0)\]
B) \[\left( a\pm \frac{a}{b}\sqrt{{{a}^{2}}+{{b}^{2}}},0 \right)\]
C) \[\left( a+\frac{a}{b}\sqrt{{{a}^{2}}+{{b}^{2}}},0 \right)\]
D) \[\left( a-\frac{a}{b}\sqrt{{{a}^{2}}+{{b}^{2}}},0 \right)\]
Correct Answer: B
Solution :
Let coordinate of the line is\[(h,0)\] and straight line is \[\frac{x}{a}+\frac{y}{v}=1.\] Given that perpendicular distance of\[bx+ay-ab=0\]from\[(h,0)\]is a \[\therefore \] \[\left| \frac{bh+a\times 0-ab}{\sqrt{{{a}^{2}}+{{b}^{2}}}} \right|=a\] \[\Rightarrow \] \[bh-ab=\pm \sqrt{{{a}^{2}}+{{b}^{2}}}\] \[\Rightarrow \] \[bh=ab\pm a\sqrt{{{a}^{2}}+{{b}^{2}}}\] \[\Rightarrow \] \[h=a\pm \frac{a}{b}\sqrt{{{a}^{2}}+{{b}^{2}}}\] \[\therefore \]Required point is\[\left( a\pm \frac{a}{b}\sqrt{{{a}^{2}}+{{b}^{2}}},0 \right)\]
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