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Question

If the point (3,4) lies on the locus of the point of intersection of the lines xcosα+ysinα=a and xsinαycosα=b where α is a variable), the point (a,b) lies on line 3x4y=0, then |a+b| is equal to

A
1
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B
7
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C
12
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D
5
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Solution

The correct option is D 7
Squaring and adding the given equations of the lines we get x2+y2=a2+b2 as the locus of the point of intersection of these lines.
Since (3,4) lies on the locus, we get
9+16=a2+b2a2+b2=25 ...(1)
Also (a,b) lies on 3x4y=0
So 3a4b=0b=(34)a ...(2)
From (1) a2+(916)a2=25a2=16
so that |a+b|2=(74)2a2=49
|a+b|=7

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