B]
To find maximum length of radius of the circle to attain wellness you need to find minimum distance between non-healthful food and origin.
For soda:
[tex] \sqrt{ {(7 - 0)}^{2} + {( - 6 - 0)}^{2} } = \sqrt{49 + 36} = \sqrt{85} [/tex]
For chips:
[tex] \sqrt{ {(8 - 0})^{2} + \sqrt{ {8 - 0}^{2} } } = \sqrt{64 + 64} = \sqrt{128} [/tex]
For fries:
[tex] \sqrt{ {( - 7 - 0)}^{2} } + \sqrt{ { (- 5 - 0)}^{2} } = \sqrt{49 + 25} = \sqrt{74} [/tex]
So, radius of circle should be less than √74.
Find maximum solution in integer numbers:
[tex] \sqrt{74} > \sqrt{64} ←→ \sqrt{74} > 8[/tex]
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C]
[tex](x_{0}, y_{0}) = (0,0); \: r = 8[/tex]
[tex](x - 0)² + (y - 0)² = 8²[/tex]
[tex]x² + y² = 64[/tex]
