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