Question

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

Answer 1

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`