Name: Mayan
Who is asking: Student
Level of the question: Secondary

Question: This is a question under Analytic Geometry, under the topic CIRCLES.

Find the standard equation of the circle that passes through the points (0,4) and (3,7) with center on the line

I've tried substituting the two points to the general equation of a circle, but I can't solve it without a third equation. The problem here is I don't really know how to use the given line of 2x-y+4=0. Please help. Thank you.



I want to think of the equation in the form

(x - h)2 + (y - k)2 = r2

This is the circle with centre (h,k) and radius r.

Since (h,k) is on the line I know that

2h - k + 4 = 0 or k = 2h + 4

Also I know that (0,4) and (3,7) are on the circle so the distance from (h,k) to (0,4) is the same as the distance from (h,k) to (3,7). Use the distance formula to write the two distances, set them equal, substitute for k using the equation above and solve for h.