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17 votes
17 votes
Find an equation of the circle whose diameter has endpoints (-2,-6) and (6,-4)

User Yannick Motton
by
2.7k points

1 Answer

21 votes
21 votes
We need to find the radius and center of the circle to create its equation. Since the diameter is the radius doubled, we just need to divide it in half to find the radius. We can do this via the midpoint formula.

Given the coordinates (-2, -6) and (6, -4) that form the diameter, we will utilize the midpoint formula to divide the segment into 1/2.

Here’s the formula:

m=(x1+x2/2, y1+y2/2)

Input the coordinates:

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

m=(2, -5)

Because (2, -5) splits the diameter into 1/2, it is the coordinates of the center. This is the first piece of information to form the equation.

Circle equation:

(x-h)^2+(y-k)^2=r^2

(h, k) is the center, r is the radius

Input the center coordinates:

(x-2)^2+(y+5)^2=r^2

Now, we have to find the radius. We will do so with the distance formula. Since a point on the circle to the center forms the radius, we will need the distance from one of the points on the circle to the center.

Distance Formula:

d=√((x2-x1)²+(y2-y1)²)

Input the coordinates (-2, -6) and (2, -5):

d=√((2+2)²+(-5+6)²)

d= √16+1

d= √17

d=4.123

Therefore, the radius is approximately 4.123. We now have all information to form the circle’s equation.

Answer:

(x-2)^2+(y+5)^2= 4.123^2
User Daniel Budick
by
3.1k points
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