Question

How do you write an equation for a circle with center (2,4) and passes through point (5, 9)?

Answer 1

`(x-2)^2 + (y-4)^2 = 34`

Explanation:

The radius can be found using Pythagoras Theorem

`r = sqrt{(5-2)^2 + (9-4)^2} = sqrt34`

For a circle with radius `r` and centered at `(a,b)`, its cartesian equation is

`(x-a)^2 + (y-b)^2 = r^2`

Therefore. for a circle with radius `sqrt34` and centered at `(2,4)`. its cartesian equation is

`(x-2)^2 + (y-4)^2 = 34`