Find the equation of the circle which passes through the points A(1, 1) and B(2, 2) and whose radius is 1. Show that there are two such circles.
Find the equation of the circle which passes through the points A(1, 1) and B(2, 2) and whose radius is 1. Show that there are two such circles.

Answer:

The general equation of a circle is,

(x – h)2 + (y – k)2 = r2 …(i)

(h, k) is the centre and r is the radius.

Putting A(1, 1) in (i)

(1 – h)2 + (1 – k)2 = 12

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

When, k = 2, h = 3 – 2 = 1

Equation of 1st circle is,

(x – 1)2 + (y – 2)2 = 1

When, k = 1, h = 3 – 1 = 2

Equation of 2nd circle is,

(x – 2)2 + (y – 1)2 = 1