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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

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

Grade:12

2 Answers

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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Badiuddin

Askiitians Expert Bharath-IITD
23 Points
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)


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

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