Question

Find the equation of the circle given that the points (−2,−1) and (4,2) are the ends of a diameter. Express your answer in the form (x−h)2+(y−k)2=F Answer as an integer or use two decimal places if necessary: Value of h (the x coordinate of the centre): Value of k (the y coordinate of the centre): Value of F

Answer 1

`d = \sqrt{ {( - 2 - 4)}^(2) + {( - 1 - 2)}^(2) } =`

`\sqrt{ {( - 6)}^(2) + {( - 3)}^(2) } = √(36 + 9) = √(45) = 3 √(5)`

`r = (3)/(2) √(5)`

`{r}^(2) = {( (3)/(2) √(5)) }^(2) = (9)/(4) (5) = (45)/(4) = 11.25`

Midpoint of diameter:

`h = ( - 2 + 4)/(2) = (2)/(2) = 1`

`k = ( - 1 + 2)/(2) = (1)/(2)`

So the center of this circle is at (1, 1/2).

The equation for this circle is:

`{(x - 1)}^(2) + {(y - .5)}^(2) = 11.25`