# How do I model this boundary problem?

by Jhon Paye   Last Updated June 30, 2020 04:20 AM

A circle of center (3,0) and radius 3 intersects another circle of center (0,0) and radius "h". Let a =(0,h) and b be the point of intersection of both in the first quadrant, (0 <h≤). If Les the line that passes through A and B, also (z, 0) is the point of intersection of L with the axis of the abscissa. Find the value of "lim h → 0 (z)"

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The point $$b$$ can be found as the point of intersection of $$x^2 + y^2 = h^2$$ and $$(x-3)^2 + y^2 = 9$$

Hence,

$$x^2 + 9 - (x-3)^2 = h^2$$

$$\implies 3(x+3) = h^2-9$$

$$\implies x = \frac{h^2 - 18}{3}$$

Corresponding $$y$$ can be obtained for point b by substituting in the equation, and then find $$z(h)$$

Dhanvi Sreenivasan
June 30, 2020 04:09 AM