Question

What is the result of isolating y^2 in the equation below (x-2)^2+y^2=64?

Answer 1

`y=\sqrt[2]{64-(x-2)^(2) }`

Explanation:

Remember that in order to isolate something form a function you just have to clear the equation for that term:

`(x-2)^2+y^2=64\\y^2=64-(x-2)^2\\y=\sqrt[2]{64-(x-2)^2}`

So the first step is clearing (x-2)^2 form that side of the equation, so since it is adding we send it to the other side withdrawing, now we are left wit y^2, after this we just have to send the exponent as a root to the other side and we finished isolating Y.

Answer 2

What is the result of isolating y^2 in the equation below (x-2)^2+y^2=64?

Solution:

We want to isolate
`y^(2)` from the equation
`(x-2)^(2) +y^(2) =64`

To isolate
`y^(2)`, we must try to get
`y^(2)` alone

So, We must subtract
`(x-2)^(2)` from both sides

`(x-2)^(2)-(x-2)^(2) +y^(2) =64-(x-2)^(2)`

`0 +y^(2) =64-(x-2)^(2)`

`y^(2) =64-(x^(2)-4x+4)`

Distributing '-' inside parenthesis

`y^(2) =64-x^(2) +4x -4`

`y^(2) =60-x^(2) +4x`