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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 the two lines is

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

The correct option is C x + a + b = 0
Equation of tangent to the parabola y2=4a(x+a) is y=m(x+a)+am..........(1)
Equation of tangent to the parabola y2=4b(x+b) is y=m1(x+b)+bm1..........(2)
Since the tangents are perpendicular mm1=1m1=1m
(2) can be written as y=(1m)(x+b)bm.......(3)
(1)(3)0=x(m+1m)+a(1+1m)+b(m+1m)x+a+b=0
Equation of the locus is x +a+b = 0

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