Question

How do you find the equation of the circle with centre at (4,-1) and passing through (0,2)?

Answer 1

`(x - 4)^2+(y+1)^2= 5^2`

Explanation:

Here is the recipe for solving this type of problem:
1) Determine Radius: Find the distance between the point on the circle and center, that is the radius
2) Write the general circle equation form: `(x - h)^2+(y-k)^2= r^2` where (h, k) is the center of the cicle

Step1 Radius - Use distance formula:
`r^2 =(x_1-x_1)^2 + (y_2-y_1)^2`
`r^2 =(4-0)^2 + (-1-2)^2 = 25`

Step2 Radius - Use distance formula:
`(x - 4)^2+(y+1)^2= 5^2`