Question

-25 Points-
If P=(3,1) and Q=(-3,-7), find the equation of the circle that has segment PQ as a diameter.

Answer 1

The diameter points are P and Q.

Find the center of the circle by finding the midpoint of P and Q:

Midpoint = (x1+x2 /2) , (y1 + y2 /2) = (3-3/2) , (1-7 /2) = (0,-3)

The center of the circle is at (0,-3)

Now find the radius, which is 1/2 the diameter.

So use the center point and one of the diameter points:

Radius= √((3-0)^2 +(1+3)^2) = 5

Now you have the center (0,-3) and radius 5.

The equation of a circle is written as (x-h)^2 + (y-k)^2 = r^2

Where h and k are the center points and r is the radius.

replace those letters with their values:

(x-0)^2 + (y - (-3))^2 = 5^2

Simplify:

x^2 + (y+3)^2 = 25

Answer 2

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:

$\rm d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$

$\rm d=\sqrt{(-3-3)^2+(-7-1)^2}$

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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