Question

Now simplify the y-terms to get the equation of the parabolic path. You do not need to expand the x-term. (2 points) Hint: Square both sides to get rid of the square roots

Answer 1

The simplified equation of $(x - 10)^2 + (y- 6)^2 = 4^2$ is $y = 6+ \sqrt{16 - (x - 10)^2}$

How to determine the simplified equation?

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The equation is given as

$(x - 10)^2 + (y- 6)^2 = 4^2$

Subtract (x - 10)^2 from both sides

$(y- 6)^2 = 4^2 - (x - 10)^2$

Evaluate 4^2

$(y- 6)^2 =16 - (x - 10)^2$

Take the square root of  both sides

$y- 6= \sqrt{16 - (x - 10)^2}$

Add 6 to both sides

$y = 6+ \sqrt{16 - (x - 10)^2}$

Hence, the simplified equation of $(x - 10)^2 + (y- 6)^2 = 4^2$ is $y = 6+ \sqrt{16 - (x - 10)^2}$

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