Question

A circle has a diameter of 12 units, and its center has been translated 4 units
up and 9 units to the left from the origin. What is the equation of the circle?

Answer 1

The equation of the circle is (x + 9)² + (y - 4)² = 36

Radius of circle

Since the circle has a diameter, d = 12 units, its radius, r = d/2 = 12/2

= 6 units.

Coordinates of center of circle

Now, since its center translated 4 units up and 9 units to the left from the origin.

It means that the y-ccordinate for its center is (0 + 4) = 4 and the x -coordinate for its center is (0 - 9) = -9

So, the center of this circle is at (-9,4)

Equation of a circle.

The equation of a circle with center (h,k) is given by

(x - h)² + (y - k)² = r² where r = radius of circle.

For our given circle,

• (h, k) = (-9, 4) and
• r = 6.

So, substituting the values of the variables into the equation, we have

(x - h)² + (y - k)² = r²

(x - (-9))² + (y - 4)² = 6²

(x + 9)² + (y - 4)² = 36

So, the equation of the circle is (x + 9)² + (y - 4)² = 36

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