Question 194701
<font face="Garamond" size="+2">


Any point on a circle is equidistant from the center, and that distance is equal to the radius of the circle.  That means the distance from (1,b) to (-2,0) must be equal to 3.  Using the distance formula:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ d = r = sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}]


Plugging in the values:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ 3 = sqrt{(1 - (-2))^2 + (b - 0)^2} = sqrt{3^2 + b^2}]


Square both sides:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ 9 = 3^2 + b^2]


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ b^2 = 0 \ \ \Rightarrow\ \ b = 0]



John
*[tex \LARGE e^{i\pi} + 1 = 0]
</font>