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Question

A line cuts the 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 and the y - axis at Q.
If AQ and BP intersect at R, the locus of R is


A

x2+y2+7x5y=0

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B

x2+y27x+5y=0

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C

5x - 7y = 35

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D

none of these

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Solution

The correct option is B

x2+y27x+5y=0


Let P(a, 0) and Q(0, b)
Slope of PQ =ba
ba×57=1 ab=57
Equation of AQ is x7+yb=1 b=7y7x
Equation of BP is xay5=1 a=5x5+y
so that 5x5+y×7x7y=ab=57 x(7x)=y(5+y)
x2+y27x+5y=0
which is the locus of R(x, y).


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