question_answer

Suppose that the points (h, k), (1,2) and (-3,4) lie on the line \[{{L}_{1}}\]. If a line \[{{L}_{2}}\] passing through the points (h, k) and (4,3) is perpendicular to \[{{L}_{1}}\], then \[\frac{k}{h}\]equals : [JEE Main 8-4-2019 Afternoon]

A) 3                                 

B) \[-\frac{1}{7}\]

C) \[\frac{1}{3}\]

D)   0

Correct Answer: C

Solution :

equation of\[{{L}_{1}}\]is \[y=-\frac{1}{2}x+\frac{5}{2}\]                      ...(1) equation of \[{{L}_{2}}\] is \[y=2x-5\]                      ..(2) by (1) and (2) \[x=3\] \[y=1\Rightarrow h=3,k=1\] \[\frac{k}{h}=\frac{1}{3}\]