Question

What is the general form of the equation of a circle given the Center (-1,2) and Solution Point (0,0)?

Answer 1

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

Explanation:

The general form for a circle with center `(a,b)` and radius `r` is
`color(white)("XXX")(x-a)^2+(y-b)^2=r^2`

With center `(-1,2)` and given that `(0,0)` is a solution (i.e. a point on the circle),
according to the Pythagorean Theorem:
`color(white)("XXX")r^2=(-1-0)^2+(2-0)^2 = 5`

and since the center is `(a,b)=(-1,2)`

by applying the general formula we get:
`color(white)("XXX")(x+1)^2+(y-2)^2=5`