Question

What is the result of isolating in the equation below?(x+4)2+y2=22

A.y2=x2-8x+6
B.y2=-82-8x+6
c.y2=-82-8x+16
D.y2=22-x2

Answer 1

The result of isolating y² in the equation (x+4)²+y²=22 is y²=-x²-8x+6, which corresponds to answer option A.

Step-by-step explanation:

The student's question asks for the result of isolating y² in the equation (x+4)²+y²=22. To do this, we need to solve for y². We start by expanding the squared binomial:

(x+4)² = x² + 8x + 16

Now, x² + 8x + 16 + y² = 22. To isolate y², we move all terms involving x to the other side of the equation by subtracting them from both sides:

y² = 22 - (x² + 8x + 16)

Combining like terms gives us:

y² = 22 - x² - 8x - 16

Further simplifying, we have:

y² = 6 - x² - 8x

Which rewrites to:

y² = -x² - 8x + 6

Therefore, the correct answer is A. y² = -x² - 8x + 6.