Question

look at the following problem and explain what Susan did incorrectly. You can explain what she did incorrectly and how to do it correctly.(Hint: It may be more than one thing.)

Answer 1

Susan has the wrong center and the wrong radius.

The center should be (3,-4) and the radius is 6.

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Reason:

Compare
`(\text{x}-3)^2 + (\text{y}+4)^2 = 36` to the template
`(\text{x}-h)^2 + (\text{y}-k)^2 = r^2`

We have

• h = 3
• k = -4
• r = 6

Susan mixed up the positive and negative signs for h and k.

It might help for her to rewrite
`(\text{x}-3)^2 + (\text{y}+4)^2 = 36` into
`(\text{x}-(3))^2 + (\text{y}-(-4))^2 = 6^2` to better spot h and k.

To find r, this is what the steps would look like

`r^2 = 36\\\\r = √(36)\\\\r = 6`

Susan might have mistakenly thought the 36 was the diameter, and further reasoned that radius = diameter/2.

That formula is indeed true. However, the 36 is not the diameter.