Question

How do you find the equation of the circle with radius 6 and center (2,4)?

Answer 1

I found: `x^2+y^2-4x-8y-16=0`

Explanation:

You can use the general relationship for the equation of a circle of center at `(h,k)` and radius `r` as:

`color(red)((x-h)^2+(y-k)^2=r^2)`

In your case:
`(x-2)^2+(y-4)^2=6^2`
`x^2-4x+4+y^2-8y+16=36`
`x^2+y^2-4x-8y-16=0`

Answer 2

`(x - 2)^2 + (y - 4)^2 = 36`

Explanation:

The standard form of the equation of a circle is.

`color(red)(|bar(ul(color(white)(a/a)color(black)( (x - a )^2 + (y - b)^2 = r^2)color(white)(a/a)|)))`
where (a , b) are the coordinates of the centre and r , the radius

in this question a = 2 , b = 4 and r = 6

substitute these values into the standard equation

`rArr (x - 2)^2 + (y - 4)^2 = 36" is the equation "`