question_answer

The coordinates of the foot of the perpendicular from \[({{x}_{1}},{{y}_{1}})\]to the line \[ax+by+c=0\] are      [Dhanbad Engg. 1973]

A)            \[\left( \frac{{{b}^{2}}{{x}_{1}}-ab{{y}_{1}}-ac}{{{a}^{2}}+{{b}^{2}}},\frac{{{a}^{2}}{{y}_{1}}-ab{{x}_{1}}-bc}{{{a}^{2}}+{{b}^{2}}} \right)\]

B)            \[\left( \frac{{{b}^{2}}{{x}_{1}}+ab{{y}_{1}}+ac}{{{a}^{2}}+{{b}^{2}}},\frac{{{a}^{2}}{{y}_{1}}+ab{{x}_{1}}+bc}{{{a}^{2}}+{{b}^{2}}} \right)\]

C)            \[\left( \frac{a{{x}_{1}}+b{{y}_{1}}+ab}{a+b},\frac{a{{x}_{1}}-b{{y}_{1}}-ab}{a+b} \right)\]

D)            None of these