Question

O(0,0), A(0,8), T(-6,0) are the vertices of ΔOAT. Find the equation of the circle that circumscribes ΔOAT?

Answer 1

The equation is: `(x-(-3))^2+ (y - 4)^2=5^2`

Explanation:

The standard Cartesian equation for a circle is:

`(x-h)^2+ (y - k)^2=r^2" [1]"`

Please observe that the y coordinate of the center of the circle, k, is the midpoint between 0 and 8:

`k = (8+0)/2`

`k = 4`

Similarly, the x coordinate of the center of the circle, h, is the midpoint between 0 and -6:

`h = (-6+0)/2`

`h = -3`

Substitute these values into equation [1]:

`(x-(-3))^2+ (y - 4)^2=r^2" [2]"`

Use the point `(0,0)` to find the value of r:

`(0-(-3))^2+ (0 - 4)^2=r^2`

`25 = r^2`

`r = 5`

Substitute into equation [2]:

`(x-(-3))^2+ (y - 4)^2=5^2" [3]"`