SOLUTION: Find by calculating the centre of a circle whose centre is on the line 7y=-2x +36 and touches both the positive x-axis and positive y-axis

Algebra ->  Quadratic-relations-and-conic-sections -> SOLUTION: Find by calculating the centre of a circle whose centre is on the line 7y=-2x +36 and touches both the positive x-axis and positive y-axis      Log On


   

Question 1044722: Find by calculating the centre of a circle whose centre is on the line 7y=-2x +36 and touches both the positive x-axis and positive y-axis
Answer by ikleyn(52794) About Me  (Show Source):
You can put this solution on YOUR website!
.
Find by calculating the centre of a circle whose centre is on the line 7y=-2x +36 and touches both the positive x-axis and positive y-axis
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 

Since the circle touches the both axes, its center lies on the bisector of the QI, which is a straght line y = x.

So, the center lies in the intersection of the two straight lines:

7y = -2x + 36,  and
y = x.

Substitute y = x into the first equation, and you will get

7y = -2y + 36,   or   9y = 36,  or y = 4.

Then x = 4, too.

Answer. The center lies at the point (4,4).