Question

The diameter of a circle has endpoints P(–7, –10) and Q(3, 2).

Answer 1

Answer:

Step-by-step explanation:

Since we are given the endpoints of the circle, the midpoint between the two endpoints will be the center of the circle. The formula for determining midpoint of a line is

Midpoint = 1/2(x1 + x2), 1/2(y1 + y2)

= 1/2(- 7 + 3), 1/2(- 10 + 2)

= (- 2, - 4)

The radius of the circle is the distance from the center to the endpoint. To determine the radius of the circle, we would apply The formula for determining the distance between two points on a straight line is expressed as

Distance = √(x2 - x1)² + (y2 - y1)²

Therefore,

Radius = √(- 2 - - 7)² + (- 4 - - 10)²

Radius = √5² + 6² = √61

A circle is the set of all points in a plane equidistant from a fixed point called the origin or center.

The center of the circle is (- 6, - 8)

The formula for determining the equation of a circle us expressed as

(x - h)² + (y - k)² = r²

Where

r represents the radius of the circle

h and k represents the x and y coordinates of the center of the circle. Comparing with the given points,

h = - 2 and k = - 4

Radius, r = √61

Substituting into the formula, it becomes

(x - h)² + (y - k)² = r²

(x - - 2)² + (y - - 4)² = √61²

(x + 2)² + (y + 4)² = 61