Question

Write the equation of the circle with center (2, 1) and (5, 2) a point on the circle. A) (x − 2)2 + (y − 1)2 = 9 B) (x − 2)2 + (y − 1)2 = 10 C) (x − 2)2 + (y − 1)2 = 16 D) (x − 2)2 + (y − 1)2 = 29

Answer 1

Option B is right.

Explanation:

We know that a circle is a locus of points keeping equal distance r from a fixed point called centre.

Here we have centre as (2,1)

Hence equation of the circle is given by

`(x-2)^2+(y-1)^2 = r^2`

To find r, we can use the fact that (5,2) lies on this circle

Hence (5,2) satisfies this equatin.

So
`(5-2)^2+(2-1)^2 = r^2`

`10 = r^2`

So equation of the circle is

`(x-2)^2+(y-1)^2 = 10`