Question

What is the equation for the translation of x2 + y2 = 64 three units to the left and two units down?

(x − 3)2 + (y − 2)2 = 64

(x + 3)2 + (y + 2)2 = 64

(x + 3)2 + (y − 2)2 = 64

(x − 3)2 + (y + 2)2 = 64

Answer 1

Answer: (x - 3)^2 + (y - 2)^2 = 64.

Explanation:

This is because to translate a point or a function in the x-axis by a certain value we need to add or subtract the value from the x variable. To translate in the y-axis we need to add or subtract the value from the y variable. In this case, we are translating it three units to the left, so we subtract 3 from x, and two units down so we subtract 2 from y.

Answer 2

Answer: The equation for the translation of x2 + y2 = 64 three units to the left and two units down is:

(x − 3)2 + (y − 2)2 = 64

Explanation:

This is known as the standard equation of a circle centered at (3, 2) with a radius of 8.

When translating a shape, we need to change the center point of the shape. If we want to translate 3 units to the left and 2 units down, it means that we need to change the center point of the shape from the origin to (3, 2). This can be achieved by subtracting 3 from x and subtracting 2 from y in the equation of the circle. This results in (x - 3)2 + (y - 2)2 = 64, which is the equation for the translated circle.