 # 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 Badiuddin askIITians.ismu Expert
148 Points
12 years ago

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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12 years ago

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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