If [tex]\( P=(-3,5) \)[/tex] and [tex]\( Q=(1,9) \)[/tex], find the equation of the circle that has segment PQ as a diameter.

[tex]\[
(x - [?])^2 + (y - [?])^2 = [\quad]
\][/tex]

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Here is the formatted version of the previous responses:

1. Electric Current and Electrons:

An electric device delivers a current of [tex]$15.0 \, \text{A}$[/tex] for 30 seconds. How many electrons flow through it?

2. Literary Symbolism:

Which best explains why Irving sets "The Adventure of the Mysterious Stranger" in a land of "masks and gondolas"?

A. The setting is symbolic of the idea that a life of quiet study is the ideal pursuit.
B. The setting is symbolic of the idea that innocence cannot be outgrown.
C. The setting is symbolic of the idea that ease and affluence are available to all.
D. The setting is symbolic of the idea that appearances can be deceiving.

3. Imagery in Poetry:

Read the lines from "The Tide Rises, The Tide Falls."

"Darkness settles on roofs and walls,
But the sea, the sea in darkness calls;"

The imagery in these lines evokes a sense of:
A. laziness
B. fear
C. mystery
D. despair

4. Solving for [tex]\( x \)[/tex]:

Solve for [tex]\( x \)[/tex].
[tex]\( 3x = 6x - 2 \)[/tex]



Answer :

Certainly! To find the equation of the circle that has segment [tex]\( PQ \)[/tex] as its diameter, we need to follow these steps:

### 1. Find the midpoint of the segment PQ:
The midpoint of a segment is given by the average of the x-coordinates and the average of the y-coordinates of the endpoints.
Given points [tex]\( P = (-3, 5) \)[/tex] and [tex]\( Q = (1, 9) \)[/tex], the midpoint, which will be the center of the circle, is calculated as:
[tex]\[ \text{Midpoint} = \left( \frac{-3 + 1}{2}, \frac{5 + 9}{2} \right) \][/tex]
[tex]\[ \text{Midpoint} = (-1.0, 7.0) \][/tex]

### 2. Find the radius of the circle:
The radius of the circle is half the length of segment [tex]\( PQ \)[/tex]. The length of [tex]\( PQ \)[/tex] can be found using the distance formula:
[tex]\[ \text{Distance} = \sqrt{(1 - (-3))^2 + (9 - 5)^2} \][/tex]
[tex]\[ \text{Distance} = \sqrt{(4)^2 + (4)^2} \][/tex]
[tex]\[ \text{Distance} = \sqrt{16 + 16} \][/tex]
[tex]\[ \text{Distance} = \sqrt{32} \][/tex]
[tex]\[ \text{Radius} = \frac{\sqrt{32}}{2} = \sqrt{8} \][/tex]

### 3. Write the equation of the circle:
The general form of the equation of a circle with center [tex]\((h, k)\)[/tex] and radius [tex]\( r \)[/tex] is:
[tex]\[ (x - h)^2 + (y - k)^2 = r^2 \][/tex]

Given:
- The center [tex]\((h, k) = (-1, 7)\)[/tex]
- The radius squared [tex]\( r^2 = 8 \)[/tex]

The equation of the circle becomes:
[tex]\[ (x + 1)^2 + (y - 7)^2 = 8 \][/tex]

Hence, the equation of the circle that has segment [tex]\( PQ \)[/tex] as its diameter is:
[tex]\[ (x + 1)^2 + (y - 7)^2 = 8.000000000000002 \][/tex]