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Question

Equation of a circle which passes through the point (2,0) and whose centre is the limit of the point of intersection of the lines 3x+5y=1 and (2+α)x+5α2y=1 as α tends to 1 is

A
25(x2+y2)+20x2y140=0
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B
25(x2+y2)20x+2y60=0
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C
9(x2+y2)20x+2y+4=0
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D
9(x2+y2)2x20y+4=0
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Solution

The correct option is C 25(x2+y2)20x+2y60=0
Solving the given equation of the lines 3x+5y=1 and (2+α)x+5α2y=1
We get x=α+13α+2=1+13+2=25 as α1
Thus, 3×25+5y=15y=165=15y=125
Henve the center of the circle is (25,125)
If r be the radius of the circle, then its equation is
(225)2+(0+125)2=r2r2=1601625
The equation of the required circle is
(x25)2+(y+125)2=160162525(x2+y2)20x+2y60=0

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