Dear sanchit
let center of circle is (h,k)
so (h+1)2 +(k)2 =25 .......1
and (h-4)2 +(h)2 =25 .........2
 
from equation 1 and 2
   (h+1)2=(h-4)2
h=3/2
put this value in equation 1
k=±5 √3/2
so two circle is possible
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Badiuddin
						

							
Dear Sanchit,
Let the circle centre be (a,b)
Now equation of that circle with radius 5 is given by
( x - a )2 + ( y - b )2 = 25......................Eq(1)
Given that this circle passes through (-1,0) and (4,0)
Then by substituting these points in the equation(1) we get
(- a - 1 )2 + b2 = 25........Eq(2) 
and 
( 4 - a )2 + b2 = 25.........Eq(3)
Substracting Eq(2) and Eq(3) gives us the value of a = 1.5
 
Now Substitute this 'a' value in either Eq(1) or Eq(2) to give two b vaues they are +2.5√3 and -2.5√3
Thus two circles are possible with centers ( 1.5 , 2.5√3 ) and ( 1.5 , -2.5√3 )
So, the answer is (b)

Please feel free to post as many doubts on our discussion forum as you can. If you find any question 
Difficult to understand - post it here and we will get you the answer and detailed solution very quickly. We 
are all IITians and here to help you in your IIT JEE preparation.

All the best !!!
 

Regards,
Askiitians Experts
Adapa Bharath