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)

Answer 2

The points on the circle which have an x-coordinate of 1 are:. (1,+√15) and (1,-√15)

The equation of a circle usually takes the form;

• (x-a)² + (y-b)² = r²

where a and b are x- and y- coordinates of the center of the circle.

In this scenario, the center is at the origin (0,0).

In essence, the points on the circle which have an x-coordinate of 1 can be evaluated as follows;

• (1-0)² + (y - 0)² = 4²

• 1 + y² = 16.

• y² = 15

• y = ±√15.

The points on the circle which have an x-coordinate of 1 are:. (1,+√15) and (1,-√15)

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