Question

How do you determine the standard form of the equation of a circle with center at (4,-1) and passing through (0, 2)?

Answer 1

`(x-4)^2+(y-1)^2=25`

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.

To establish the equation , we require the radius. The length of the line joining the centre and point on the circumference (0 ,2) is the radius.
Using the `color(blue)"distance formula"` on the points (4 ,-1) and (0 ,2)

`d=sqrt((0-4)^2+(2+1)^2)=sqrt25=5" equals r"`

`rArr(x-4)^2+(y-1)^2=25" is the equation of the circle "`