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Question

The equations of one of the straight lines which pass through the point 1,3 and make an angle tan-12 with the straight line, y+1=32x is:


A

52x+4y-15+42=0

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B

42x-5y-5+42=0

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C

42x+5y-42=0

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D

42x+5y-15+42=0

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Solution

The correct option is D

42x+5y-15+42=0


Explanation for correct option:

Let the equation of the straight line is y=mx+c

The straight line passes through 1,3

3=m+c

Given that the equations of one of the straight lines which pass through the point 1,3 and make an angle tan-12 with the straight line, y+1=32x

From the given figure,

tantan-12=m-321+3m22=m-321+3m2

For positive

2=m-321+3m26m+2=m-325m=-42m=-425

For negative

6m+2=-m+327m=22m=227

For m=-425

c=3-m=15+425

y=-42x5+15+42542x+5y-15+42=0

For m=227

c=3-m=21-225

y=22x7+21-2277y-22x-21-22=0

Hence, option D is correct.


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