Question

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

Answer 1

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

$y^{2} =64-x^{2} +4x -4$

$y^{2} =60-x^{2} +4x$

Answer 2

Answer:

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

Step-by-step 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.