Question

A diameter of a circle has endpoints P(-10,-2) and Q(4,6).

Answer 1

Answer:

a. (-3,2)

b. sqrt(65)

c. (x + 3)² + (y - 2)² = 65

Step-by-step explanation:

Centre:

midpoint of the diameter

(h,k) = (-10+4)/2, (-2+6)/2

(h,k) = (-3,2)

Length of the diameter:

sqrt[(-2-6)² + (-10-4)²]

sqrt(260)

2sqrt(65)

Radius: ½ × diameter

Radius = sqrt(65)

Equation:

(x - h)² + (y - k)² = r²

(x - -3)² + (y - 2)² = (sqrt(65))²

(x + 3)² + (y - 2)² = 65

Answer 2

Answer:

a. (-3, 2).

b.  √65

c.  (x + 3)^2 + (y - 2)^2 = 65

Step-by-step explanation:

a.  The center is the midpoint  of the diameter PQ.

= (-10+4)/2, (-2+6)/2

= (-3, 2).

b. The radius is the distance from the center to a point on the circle.

Take the point (4, 6):

The radius = √((-3-4)^2 + (2-6)^2)

= √65.

c.  The equation of the circle is:

Using the standard form

(x - h)^2 + (y - k)^2 = r^2  where  (h, k) is the center and r = the radius:

it is (x - (-3)^2 + (y - 2) = 65

= (x + 3)^2 + (y - 2)^2 = 65.