Answer:
One point that is also on the circle is 7 + 18i.
Explanation:
Data:
End points of diameter at 3+ 18i and 7 – 6i.
Calculations
Centre of circle:
The centre is at the middle of the end points.
(x, y) = ((x₁ + x₂)/2, (y₁ + y₂)/2)
= ((3+7)/2, (18i – 6 i)/2))
= (10/2, 12i/2)
= (5, 6i)
Radius:
The centre is at (5, 6i). A point on the circumference is (3, 18i)
The distance between the two points is given by
r² = (x₂ - x₁)² + (y₂ - y₁)²
= (3 - 5)² + (18 - 6)²
= (-2)² + (12)²
= 4 + 144
= 148
r = √148
Equation for circle
The general equation for a circle is
(x – h)² + (y - k)² = r² Substitute values for h, k
( x - 5)² + (y - 6)² = 148
Points on circle:
Any point that satisfies the above equation is a point on the circle.
There are many solutions, but one point that works is 7 + 18i (see graph below).
For example,
(7 - 5)² + (18 - 6)² = 2² + 12² = 4 + 144 = 148