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#40080

transformations

circles

hard

240 sec

Circle A (shown), a circle with its center at $(- 2, 0)$ and a radius of $3$ , is defined by the equation $(x + 2)^{2} + y^{2} = 9$ . Circle B (not shown) is the result of shifting circle A so its new center is at $(1, - 4)$ , and its radius is $\frac{2}{3}$ times the radius of circle A. What is the value of $r^{2}$ for circle B, where $r$ is the radius of circle B?

• Up to 5 characters (6 if negative). Only numbers, decimal (.), fraction (/), negative (-).
• Fractions must be in lowest terms.
• Mixed numbers must be converted to improper fractions.