Question

find the eqution of cicle which passes through two points on the x axes which are at distance 4 from the origen and whose radius is 5​

Answer 1

Answer:

There are two circles which pass through two points A and A' on the x-axis which are at a distance of 4 units from the origin.

The center of there circles lie on the y-axis

In ΔOAC,AC

2

=OA

2

+OC

2

⇒5

2

=4

2

+OC

2

⇒OC

2

=5

2

−4

2

=25−16=9

∴OC=3 units

So, the coordinates of the centers of the required circles are C(0,3) and C'(0,-3)

Hence, the equation of the required circles are (x−0)

2

+(y±3)

2

=5

2

⇒x

2

+y

2

±6y−16=0