The number of circles having radius 5 and passing through the points (-1, 0) and (4,0) is (a) 1 (b) 2 (c) 4 (d) infinite

							
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)

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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.

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Adapa Bharath