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  • The nearest point on the line  from the origin is -<str

The nearest point on the line 3 x+4 y=12 from the origin is -

Option: 1

\left(\frac{36}{25}, \frac{48}{25}\right)


Option: 2

\left(3, \frac{3}{4}\right)


Option: 3

\left(2, \frac{3}{2}\right)


Option: 4

none of these


Answers (1)

best_answer

If ‘D’ be the foot of altitude, drawn from origin to the given line, then ‘D’ is the required point.
Let \angle \mathrm{OBA}=\theta \Rightarrow \tan \theta=\frac{4}{3} \Rightarrow \angle \mathrm{DOA}=\theta  we have  \mathrm{OD}=\frac{12}{5}
If D is (h, k) then h = OD  \cos \theta, k=O D \sin \theta \Rightarrow \mathrm{h}=\frac{36}{25}, \mathrm{k}=\frac{48}{25}

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