The missing value is 5² or 25 if the P=(3,1) and Q=(-3,-7), find the equation of the circle that has segment PQ as a diameter.
What is a circle?
It is described as a set of points, where each point is at the same distance from a fixed point (called the center of a circle)
We have a circle equation:
x² + (y + 3)² = ?
As we know the standard form of the circle equation is:
(x - h)² + (y - k)² = r²
Here (h, k) is the center of the circle and r is the radius of the circle.
The points are P (3, 1) and Q(-3, -7)
The segment PQ is the diameter of the circle
The distance between PQ is:
Using the distance formula:
[tex]\rm d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
[tex]\rm d=\sqrt{(-3-3)^2+(-7-1)^2}[/tex]
d = √(36 + 64)
d = √100
d = 10 units
The radius of the circle r = d/2
r = 10/2
r = 5 units
Plug the value of r in the equation:
x² + (y + 3)² = 5²
Thus, the missing value is 5² if the P=(3,1) and Q=(-3,-7), find the equation of the circle that has segment PQ as a diameter.
Learn more about circle here:
brainly.com/question/11833983
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