Question

Tammy has planted a small, young tree in her yard. To allow for the tree’s growth, she needs 15 feet in all directions around the base of the tree to remain open and unplanted. Which best describes the section of ground surrounding the base of the tree that should remain unplanted?

Answer 1

Answer:

First, remember that a circle of radius R centered in the point (a, b) can be written as:

(x - a)^2 + (y - b)^2  = R^2

Suppose that we can model the yard as a rectangular coordinate axis.

And the tree is planted in the point (a, b)

If we want to have 15 feet in all directions around the base of the tree (15 ft around the point (a, b))

The section that must remain unplanted is:

(x - a)^2 + (y - b)^2   ≤ R^2

Where the ≤ symbol is used because all the interior of the circle must remain unplanted (border included)

Answer 2

The equation that best describes the situation is $(x -a)^2 + (y - b)^2 \le 225$

15 feet in all direction around the base of the tree means that, the radius across the circumference is 15.

So, we have:

$r = 15$

The situation can then be modeled by the following equation of circle

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

From the question, we understand that the section remains open and unplanted.

So, the above equation becomes

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

Substitute 15 for r

$(x -a)^2 + (y - b)^2 \le 15^2$

Evaluate the exponent

$(x -a)^2 + (y - b)^2 \le 225$

Hence, the equation that best describes the situation is $(x -a)^2 + (y - b)^2 \le 225$

Read more about circle equations at:

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