Question

Find the equation of the circle with radius 5 whose centre lies on x -axis and passes through the point (2, 3).

Answer 1

The given radius of the circle is 5, its center lies on x- axis and passes through the point ( 2,3 )

So, k=0,r=5 .

The equation of the required circle is given by,

( x−h ) 2 + ( y ) 2 = r 2

Where h and k denotes the center of the circle and r denotes the radius of the circle.

Since circle also passes through the point ( 2,3 ) , this point will satisfy the equation of the circle represented in equation ( 1 )

( 2−h ) 2 + ( 3 ) 2 =25 ( 2−h ) 2 =16 2−h=± 16 2−h=±4

If 2−h=4 then h=−2

If 2−h=−4 then h=6

Substitute h=−2 in (1) to determine the equation of the circle,

( x+2 ) 2 + y 2 =25 x 2 +4+4x+ y 2 =25 x 2 +4x+ y 2 −21=0

Substitute h=6 in (1) to determine the equation of the circle,

( x−6 ) 2 + y 2 =25 x 2 +36−12x+ y 2 =25 x 2 −12x+ y 2 +11=0

Thus the equation of the circle with radius 5 whose center lies on x- axis and passes through the point ( 2,3 ) is x 2 +4x+ y 2 −21=0 when h=−2 and x 2 −12x+ y 2 +11=0 when h=6 .