Question 1.13: Find an equation for (a) a circle of radius 4 with center at...
Find an equation for (a) a circle of radius 4 with center at (-2, 1), (b) an ellipse with major axis of length 10 and foci at (-3, 0) and (3, 0).
(a) The center can be represented by the complex number -2 + i. If z is any point on the circle [Fig. 1-20], the distance from z to -2 + i is
|z-(-2+i)|=4Then |z+2-i|=4 is the required equation. In rectangular form, this is given by
|(x+2)+i(y-1)|=4, \quad \text { i.e., }(x+2)^2+(y-1)^2=16(b) The sum of the distances from any point z on the ellipse [Fig. 1-21] to the foci must equal 10. Hence, the required equation is
|z+3|+|z-3|=10
In rectangular form, this reduces to x^2 / 25+y^2 / 16=1 (see Problem 1.74)
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