Answer:
A) find its center = (3, 2)
B) find the radius of the circle = √104
C) find the equation of the circle = x² + y² - 6x - 4y -91 = 0
Step-by-step explanation:
A)- The center must be the mid-points of (-2, 1) and (8, 3).
So, using the equation of mid-point,
Here, (x₁, y₁) = (-2, 1) and (x₂, y₂) = (8, 3)
Putting these value in above equation. We get,
h = 3 and k = 2
Thus, Center = (h, k) = (3, 2)
B)- For finding the radius we have to find the distance between center and any of the end point.
Thus using Distance Formula,
⇒ Radius = √104 = 2√26
C)- The equation of circle is determined by formula:
where (h, k ) is center of circle and
r is the radius of circle.
⇒ (x - 3)² + (y - 2)² = 104
⇒ x² + y² - 6x - 4y -91 = 0
which is the required equation of the circle.