How do you write an equation of a circle with Center (-1, 15) Point on Circle (2, 13)?

Question

4164 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-11-24T17:53:51

#(x+1)^2 + (y-15)^2= 13#

If 'r' is the radius of the circle then its equation would be

#(x+1)^2 +(y-15)^2 =r^2#

Since point (2,13) lies on the circle, it must satisfy the above equation. Thus

#(2+1)^2+(13-15)^2 =r^2#
#9+4= 13=r^2#

Thus the equation of the circle becomes
#(x+1)^2 + (y-15)^2= 13#

Answer 2 · 2016-11-24T17:53:55

Please see the explanation.

Use the standard equation of a circle:

#(x - h)^2 + (y - k)^2 = r^2#

where #(x,y)# is any point on the circle, #(h,k)# is the center, and r is the radius.

You are not given r, therefore, you must substitute the given point and the center into the standard form, and then compute value of r.

#(2 - -1)^2 + (13 - 15)^2 = r^2#

#3^2 + (-2)^2 = r^2#

#r^2 = 9 + 4#

#r^2 = 13#

#r = sqrt(13)#

The equation of the circle is:

#(x - -1)^2 + (y - 15)^2 = (sqrt(13))^2#