How do you write the equation for a circle with center at (2,-5) and passing through (3,4)?
1 Answer
Jun 10, 2016
Explanation:
The general equation of a circle is:
#color(blue)(|bar(ul(color(white)(a/a)(x-h)^2+(y-k)^2=r^2color(white)(a/a)|)))# where:
#x=# x-coordinate
#h=# x-coordinate of centre
#y=# y-coordinate
#k=# y-coordinate of centre
#r=# radius
Start by plugging
#(x-(2))^2+(y-(-5))^2=r^2#
Replace
#(3-2)^2+(4-(-5))^2=r^2#
Simplify.
#(1)^2+(9)^2=r^2#
#1+81=r^2#
#21=r^2#
Rewrite the equation by including the centre and the radius.
#(x-2)^2+(y-(-5))^2=21#
#color(green)(|bar(ul(color(white)(a/a)color(black)((x-2)^2+(y+5)^2=21)color(white)(a/a)|)))#