Question

7- a. What is the radius of the circle with center (3,10) that passes through (12,12)?

b. What is the equation of this circle?

Answer 1

Answer: a. Radius of circle =
`√(85)`

b. The equation of this circle :
`(x-3)^2+(y-10)^2=85`

Explanation:

Given : Center of the circle = (3,10)

Circle is passing through (12,12).

a. To find the radius we apply distance formula (∵ Radius is the distance from center to any point ion the circle.)

Radius of circle =
`√((12-3)^2+(12-10)^2)`

Radius of circle =
`√((9)^2+(2)^2)=√(81+4)=√(85)`

i.e. Radius of circle =
`√(85)`

b. Equation of a circle =
`(x-h)^2+(y-k)^2=r^2` , where (h,k)=Center and r=radius of the circle.

Put the values of (h,k)= (3,10) and r=
`√(85)` , we get

`(x-3)^2+(y-10)^2=(√(85))^2`

`(x-3)^2+(y-10)^2=85`

∴ The equation of this circle :
`(x-3)^2+(y-10)^2=85`