Kevin's work for deriving the equation of a circle is shown below. x2 + 4x = −(y2 − 20) step 1 x2 + 4x = −y2 + 20 step 2 x2 + 4x

Question

4 years ago

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Kevin's work for deriving the equation of a circle is shown below. x2 + 4x = −(y2 − 20) step 1 x2 + 4x = −y2 + 20 step 2 x2 + 4x

+ 4 = −y2 + 20 − 4 step 3 (x + 2)2 = −y2 + 20 − 4 step 4 (x + 2)2 + y2 = 16 in which step did he make an error in his work

Mathematics

1 answer:

SVEN [57.7K] · Answer 1 · 2022-01-11T22:10:58+03:00

We have the following equation:
x2 + 4x = - (y2 - 20)
Let's review step by step:
step 1:
x2 + 4x = -y2 + 20
Answer: OK
step 2:
x2 + 4x + 4 = -y2 + 20 - 4
Answer: Wrong
The correct step is:
x2 + 4x - 4 = -y2 + 20 - 4
Or equivalently:
x2 + 4x + 4 = -y2 + 20 + 4
Answer:
he did make an error in his work in step 2