Q.
If from P(4,4) perpendiculars to the straight lines 3x+4y+5=0 and y=mx+7 meet at Q and R and area of triangle PQR is maximum, then m is equal to
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a
4/3
b
−3/4
c
−1
d
1
answer is A.
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Detailed Solution
since PQ is of fixed lengtharea of ΔPQR=12|PQ||RP|sinθThis will be maximum if sinθ=1&RP is maximum.Since line y=mx+7 rotates about(0,7) , if PR' is perpendicular to the line than PR’ is maximum value of PR.∴m=−(4−04−7)=43.
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