Answer:
1. The location of the center of the given circle = The origin (0, 0)
The given points on the circumference of the circle = (1, √3), and (0, -2)
The general form of the equation of a circle, is presented as follows
(x - h)² + (y - k)² = r²
Where;
(h, k) = The coordinates of the center of the circle
r = The radius of the circle
∴ (h, k) = (0, 0)
The radius of the given equation is the distance from the center (0, 0) to either the point (0, -2) or (1, √3)
The distance from the center (0, 0) to the point (0, -2), which are points on the same ordinate, r = y₂ - y₁
∴ r = 0 - (-2) = 2
r = 2
The equation of the circle is therefore;
(x - 0)² + (y - 0)² = 2²
∴ x² + y² = 2²
2. When x = 1, and y = √3, we have;
(1 - 0)² + (√3 - 0)² = 1 + 3 = 4 = 2²
When x = 0, and y = -2, we have;
(0 - 0)² + ((-2) - 0)² = (-2)² = 4 = 2²
Therefore, the points shown on the circle (1, √3), and (0, -2) satisfy the equation of the circle, x² + y² = 2² and are solutions to the equation of the circle
Step-by-step explanation:
=