Let a 2 − bm 2 + 2 d + 1 = 0 , where a, b, d are fixed real numbers such that a + b = d 2 . If the line x + my + 1 = 0 touches a fixed circle then find the equation of circle
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x 2 + y 2 – 2dx + d 2 – b = 0
Sol. a 2 – bm 2 + 2 d + 1 = 0 ......
and a + b = d 2 .......
Put a = d 2 – b in equation , we get ( d + 1) 2 = b( 2 + m 2 )
⇒ 
= 
......
From we can say that the line x + my + 1 = 0 touches a fixed circle having centre at (d,0) and radius= 
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