Angles made with the X-axis by the two lines passing through the point P (1 ,2 ) and cutting the line x+y=4 at a distance 63 units from the point P are

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Accepted Answer

Correct answer: C. (c) Let slope of line =m Equation of line is y-2=m (x-1 ) y-2= mx-m mx-y+ (2-m )=0 On solving mx-y+ (2-m ) and x+y=4, we get the coordinates ( m+2m+1 , 3m+2m+1 ). Now, it is given that Distance= ( m+2m+1-1)^2+( 3m+2m+1-2)^2= 63 1 (m+1 )^2+ m^2 (m+1 )^2= 69 1+m^2 (m+1 )^2= 23 3+3m^2=2m^2+4m+2 m^2-4m+1=0 m=2+ 3 ,2- 3 tan ⁡ =2- 3 = 12 ; tan ⁡ =2+ 3 = 5 12

$Angles made with the X -axis by the two lines passing through the point P (1, 2) and cutting the line x + y = 4 at a distance \frac{6}{3} units from the point P are$

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