Answered

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What is the result of isolating [tex]y^2[/tex] in the equation below?

[tex]\[ (x-2)^2 + y^2 = 64 \][/tex]

A. [tex]y^2 = -x^2 + 4x + 4[/tex]
B. [tex]y^2 = -x^2 + 4x + 60[/tex]
C. [tex]y^2 = 64 - (x-2)^2[/tex]
D. [tex]y^2 = x^2 + 4x + 60[/tex]

Sagot :

GinnyAnswer
Let's isolate \( y^2 \) in the given equation:
[tex]\[ (x-2)^2 + y^2 = 64 \][/tex]

First, we subtract \( (x-2)^2 \) from both sides of the equation:
[tex]\[ y^2 = 64 - (x-2)^2 \][/tex]

Next, we expand \( (x-2)^2 \):
[tex]\[ (x-2)^2 = x^2 - 4x + 4 \][/tex]

Now we substitute the expanded form back into the equation:
[tex]\[ y^2 = 64 - (x^2 - 4x + 4) \][/tex]

Simplify by distributing the negative sign:
[tex]\[ y^2 = 64 - x^2 + 4x - 4 \][/tex]

Combine like terms:
[tex]\[ y^2 = 60 - x^2 + 4x \][/tex]

So, we have:
[tex]\[ y^2 = -x^2 + 4x + 60 \][/tex]

Therefore, the correct answer matches option B:
[tex]\[ y^2 = -x^2 + 4x + 60 \][/tex]
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