Question

A circle is centered at the origin (0,0) and has a radius of 4 units. Which points on the circle have an x-coordinate of 1? (Your answer should be a list of points, such as "(1,1), (2,4)".)

Answer 1

Answer: (1, √15) and (1, -√15)

Step-by-step explanation:

A circle centered at the point (a, b) of radius R can be written as:

(x - a)^2 + (y - b)^2 = R^2

In this case we have:

"A circle is centered at the origin (0,0) and has a radius of 4 units"

Then the equation for this circle is:

x^2 + y^2 = 4^2 = 16.

Now, we want to find the points where x = 1, then we can replace that value and solve the equation for y.

1^2 + y^2 = 16

1 + y^2 = 16

y^2 = 16 - 1 = 15

y = +-√15

Then the two points that have the x-coordinate equal to 1 are:

(1, √15) and (1, -√15)