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Question

Two straight lines are perpendicular to each other one of them touches the parabola y2=4a(x+a) and the other touches y2=4b(x+b). The locus of the point of intersection of these two lines is

A
x+a+b=0
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B
xab=0
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C
x=0
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D
x+a=0
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Solution

The correct option is A x+a+b=0
Let m be the slope of one line, then slope of other line will be 1m
Equation of the line touching the parabola y2=4a(x+a) is
y=m(x+a)+am(1)
Equation of the line touching the parabola y2=4b(x+b) is
y=1m(x+b)+b1m
y=1m(x+b)bm(2)
Solving equation (1) and (2) we get
am+m(x+a)=bm1m(x+b)
x(m+1m)+a(m+1m)+b(m+1m)=0
x+a+b=0 [m+1m0]

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