Question

A machine part is a 4-in.-square piece of metal plate with a round hole 2 in.in diameter drilled through the center. What is the equation of the circle given that the placed is Quadrant 1 with its corner at the origin?

Answer 1

The round hole in the square machine part is an inscribed circle

The equation of the circle is $(x - 2)^2 + (y - 2)^2 = 1$

How to determine the equation of the circle

The corner of the square machine part is said to be at the origin.

This means that, the coordinates of the machine parts are:

(x,y) = (0,0), (4,0), (4,4) and (0,4)

Calculate the midpoint of the diagonals, to determine the midpoint of the circle.

(x,y) = 0.5 * (0 + 4, 4 + 0)

This gives

(x,y) = (2,2)

The diameter of the circle is:

d = 2 inches

Divide by 2 to calculate the radius

r = 1 inch

The equation of a circle is represented as:

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

Where:

Center = (x,y) = (a,b) = (2,2)

So, we have:

$(x - 2)^2 + (y - 2)^2 = 1^2$

Evaluate the square of 1

$(x - 2)^2 + (y - 2)^2 = 1$

Hence, the equation of the circle is $(x - 2)^2 + (y - 2)^2 = 1$

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