Find The Value Of k so That The Straight Line 2x + 3y + 4 + k (6x – y + 12) = 0 And 7x + 5y – 4 = 0 Are Perpendicular To Each Other.

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Question

Find the value of k so that the straight line 2x + 3y + 4 + k (6x – y + 12) = 0 and 7x + 5y – 4 = 0 are perpendicular to each other.

Solution

Correct option is

Given line are

(2 + 6k)x + (3 – k)y + 4 + 12k = 0                            … (i)

and 7x + 5y – 4 = 0                                                  … (ii)  

     

and slope of line (ii) m2 = –7/5   

since line (i) is perpendicular to line (ii) 

or 14 + 42k = 5k – 15 or 37k = –29 or k = –29/37

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