Questions
Two of the lines represented by are perpendicular for
a
all real values of d
b
two real values of d
c
three real values of d
d
no real value of d
detailed solution
Correct option is B
Let m1,m2,m3 be the slopes of the three lines represented by the given equation such that m1m2=−1We have m1m2m3=−1d so that m3=1dSince y=m3x i.e. x=dy satisfies the given equation, we getd3−6d2+3d+d =0⇒ dd2−6d+4 =0If d=0 the given equation represents the lines x = 0 and x2−6xy+3y2=0 which are not perpendicular.∴d≠0 and d2−6d+4=0⇒ d=6±36−162=3±5which gives two real values of d.Talk to our academic expert!
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The two lines represented by are perpendicular to each other for
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