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Question

Let PQR be a right angled isosceles triangle right angled at P(2,1). If the equation of the line QR is 2x+y=3, then the equation representing the pair of lines PQ and PR is


A

3x23y2+8xy+20x+10y+25=0

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B

3x23y2+8xy20x10y+25=0

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C

3x23y2+8xy+10x+15y+20=0

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D

3x23y28xy10x15y20=0

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Solution

The correct option is B

3x23y2+8xy20x10y+25=0


Let the slopes of PQ and PR be m and 1m respectively. Since PQR is an isosceles triangle PQR=PRQ

m+212m=1m+21+2m
[ slope of QR = -2]
m+2=±(12m)m=3 or 13
So the equations of PQ and PR are
(y1) = 3(x2) and y1=(13)(x2)


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