Consider the graph of the parabola y = x. (a) Find the radius r of the largest
Question:
Consider the graph of the parabola y = x².
(a) Find the radius r of the largest possible circle centered on the y-axis that is tangent to the parabola at the origin, as shown in the figure. This circle is called the circle of curvature. Find the equation of this circle. Use a graphing utility to graph the circle and parabola in the same viewing window to verify your answer.
(b) Find the center (0, b) of the circle of radius 1 centered on
the y-axis that is tangent to the parabola at two points, as
shown in the figure. Find the equation of this circle. Use a
graphing utility to graph the circle and parabola in the same
viewing window to verify your answer.
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a b x y r r Circle x y Parabola Sub...View the full answer
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