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If the point P is symmetric to the point Q(4,-1) with respect to the bisector of the first quadrant then the length of PQ is

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The correct Answer is:
`a to p, s;" b" to q,s; " c" to p,r; " d" to s`
a. The given lines are concurrent. So,
`|{:(3, 1, -4),(1, -2, -6),(lambda, 4, lambda^(2)):}| = 0`
`"or " lambda^(2) +2lambda-8 =0`
`"or " lambda=2, -4`
b. The points are collinear. Hence,
`|{:(lambda+1, 1, 1),(2lambda+1, 3, 1),(2lambda+2, 2lambda, 1):}| = 0`
`"or " 2lambda^(2) - 3lambda-2 =0 " or " lambda = 2, -(1)/(2)`
c. The point of intersection of x-y=1 and 3x+y-5=0 is (1,2). It lines on the line
`x+y-1-|(lambda)/(2)| = 0 " "therefore lambda = +-4`
d. The midpoint of (1, -2) and (3, 4) will satisfy
`y-x-1+lambda=0`
`therefore lambda = 2`
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