Question 1044722
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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
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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.

<U>Answer</U>. The center lies at the point (4,4).
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