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Question

A line cuts x-axis at A(7,0) and the y-axis at B(0,5). A variable line PQ is drawn perpendicular to AB cutting the x-axis at P(a,0) and the y-axis at Q(0,b). If AQ and BP intersect at R, the locus of R is 


A
x2+y2+7x+5y=0
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B
x2+y2+7x5y=0
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C
x2+y27x+5y=0
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D
x2+y27x5y=0
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Solution

The correct option is C x2+y27x+5y=0
Slope of the line AB is 57
Slope of the line PQ
ba=75ba=75
Equation of the line
BP:xay5=11a=5+y5x(1)
Equation of the line
AQ:x7+yb=11b=7x7y(2)
solving above equations we get 
x2+y27x+5y=0
 

Mathematics

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