Answer:
The equation of the circle in standard form is: (x - 2)² + (y - 4)² = 9
Step-by-step explanation:
* Lets revise the standard form of the equation of the circle
- If the center of the circle is point (h , v) and the radius of the
circle is r, then the standard form of the equation of the circle
is (x - h)² + (y - v)² = r²
- (x , y) a general point on the circle
* Lets look to the picture
- The center of the circle is point (2 , 4)
- The highest point on the circle is (2 , 7) and the lowest point
on the circle is (2 , 1)
∴ The diameter of the circle = 7 - 1 = 6
∵ The radius = 1/2 the diameter
∴ The radius of the circle = 1/2 × 6 = 3
* Now we can write the equation of the circle
∵ h = 2 and v = 4
∵ r = 3
∴ (x - 2)² + (y - 4)² = 3²
∴ The equation of the circle in standard form is:
(x - 2)² + (y - 4)² = 9
