A) \[\left( \frac{81}{25},\frac{92}{25} \right)\]
B) \[\left( \frac{92}{25},\frac{81}{25} \right)\]
C) \[\left( \frac{46}{25},\frac{54}{25} \right)\]
D) \[\left( \frac{-81}{25},\frac{-92}{25} \right)\]
E) \[\left( \frac{81}{25},\frac{108}{25} \right)\]
Correct Answer: A
Solution :
Let M be the foot of perpendicular from P(3, 4) on the line\[3x-4y+5=0\]. Then M is the point of intersection of\[3x-4y+5=0\]and line passing through P (3, 4) and perpendicular to \[3x-4y+5=0\] ...(i) Equation of line perpendicular to \[3x-4y+5=0\]is \[4x+3y+\lambda =0\] This passes through (3, 4) \[\Rightarrow \] \[12+12+\lambda =0\] \[\Rightarrow \] \[\lambda =-24\] \[\therefore \]Equation is \[4x+3y-24=0\] ...(ii) On solving Eqs. (i) and (ii), we get \[y=92/25,\text{ }x=81/25\] \[\therefore \]Required point is (81 / 25, 92/ 25).
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