Exercise 30 Page 648

To write the equation of a circle, we need its center and its radius. Let's calculate these two things one at a time.

Center

The center of a circle is the midpoint of the endpoints of a diameter.

Therefore, to find the coordinates of the center (h,k) we will substitute the given points into the Midpoint Formula.

The center of the circle is (1, 52).

Radius

The radius of a circle is half its diameter.

To find it, we can find the distance between the center and any known point on the circumference of the circle. For simplicity, we will use (0,0). Let's substitute this point and the center into the Distance Formula.

Because the distance is sqrt(29)2, we know that the radius is sqrt(29)2.

Equation

Let's recall the general equation of a circle with center ( h, k) and radius r. (x- h)^2+(y- k)^2= r^2 We can substitute the values found above into this equation. (x - 1 )^2 + (y - 5/2)^2 = ( sqrt(29)/2)^2 ⇕ (x - 1 )^2 + (y - 5/2)^2 =29/4