# 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

148 Points
14 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

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.

All the best.

Regards,

23 Points
14 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 )

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

All the best !!!

Regards,