Question

Which of the following could be the center of a circle that includes the points (-5, 2) and (-3, 6)?

A. (0, 2)
B. (0, -2)
C. (2, 2)
D. (2, 1)

Answer 1

The center of a circle that includes the points (-5, 2) and (-3, 6) could be (a) (0,2)

How to determine the center of the circle?

The points are given as:

(-5, 2) and (-3, 6)

The equation of  a circle is represented as:

$(x -a)^2 + (y - b)^2 = r^2$

Where:

• Points = (x,y)
• Center = (a,b)
• Radius = r

Substitute both points in the above equation

$(-5 + a)^2 + (2 - b)^2 = r^2$

$(- 3+ a)^2 + (6 - b)^2 = r^2$

The radii are equal.

So, we have:

$(-5 + a)^2 + (2 - b)^2 = (- 3+ a)^2 + (6 - b)^2$

Expand the equations

$25 -10a + a^2 + 4 - 4b + b^2 = 9 - 6a + a^2 + 36 - 12b + b^2$

Evaluate the like terms

$25 -10a + 4 - 4b = 9 - 6a + 36 - 12b$

Collect like terms

6a -10a - 4b + 12b = 9  + 36  - 25 - 4

Evaluate

-4a + 8b = 16

Divide through by - 4

a - 2b = -4

Next, we test the options:

Option (a) (a,b) = (0,2)

Substitute these values in the equation

0 - 2*2 = -4

Evaluate

-4 = -4

Both sides of the equation are the same

Hence, the center of a circle that includes the points (-5, 2) and (-3, 6) could be (a) (0,2)

Read more about circle equations at:

https://brainly.com/question/1559324

#SPJ1