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write the standard form of the equation of the circle with the given characteristics center (-3,-8) solution point (1,-11)

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Explanation:

general equation of the circle is


{(x - a)}^(2) + {(y - b)}^(2) = {r}^(2)

a and b are the x and y coordinates of the centre respectively. Now plug them in


{(x - ( - 3))}^(2) + {(y - ( - 8))}^(2) = {r}^(2) \\ {(x + 3)}^(2) + {(y + 8)}^(2) = {r}^(2)

To get the value of the square radius you can substitute the given points


{(1 + 3)}^(2) + {( - 11 + 8)}^(2) = {r}^(2) \\ 16 + 9 = {r}^(2) \\ {r }^(2) = 2

Theredore our Equation will be


{(x + 3)}^(2) + {(y + 3)}^(2) = 25

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