Question

Determine the equation of the circle graphed below.

Answer 1

`\displaystyle \large{(x-3)^2+(y+7)^2=9}`

Explanation:

By looking at the graph, we can say that the circle has a center point at (3,-7). Next, find the radius which is the distance between center and an endpoint.

Distance Formula

`\displaystyle \large{√((x_2-x_1)^2+(y_2-y_1)^2)}`

Determine:

• Center =
  `\displaystyle \large{(x_2,y_2)}` = (3,-7)
• Endpoint =
  `\displaystyle \large{(x_1,y_1)}` = (0,-7)

Therefore:

`\displaystyle \large{√((3-0)^2+(-7-(-7))^2)}\\\\\displaystyle \large{√(3^2+(-7+7)^2)}\\\\\displaystyle \large{√(9) = 3}`

Therefore, radius = 3.

Equation of Circle

`\displaystyle \large{(x-h)^2+(y-k)^2=r^2}`

where:

• (h,k) = center = (3,-7)
• r = 3 so r² = 9

Hence:

`\displaystyle \large{(x-3)^2+(y-(-7))^2=3^2}\\\\\displaystyle \large{(x-3)^2+(y+7)^2=9}`