What is the result of isolating y^2 in the equation below (x-2)^2+y^2=64?
Solution:
We want to isolate [tex] y^{2} [/tex] from the equation [tex] (x-2)^{2} +y^{2} =64 [/tex]
To isolate [tex] y^{2} [/tex], we must try to get [tex] y^{2} [/tex] alone
So, We must subtract [tex] (x-2)^{2} [/tex] from both sides
[tex] (x-2)^{2}-(x-2)^{2} +y^{2} =64-(x-2)^{2} [/tex]
[tex] 0 +y^{2} =64-(x-2)^{2} [/tex]
[tex] y^{2} =64-(x^{2}-4x+4) [/tex]
Distributing '-' inside parenthesis
[tex] y^{2} =64-x^{2} +4x -4 [/tex]
[tex] y^{2} =60-x^{2} +4x [/tex]
Answer:
[tex]y=\sqrt[2]{64-(x-2)^{2} }[/tex]
Step-by-step explanation:
Remember that in order to isolate something form a function you just have to clear the equation for that term:
[tex](x-2)^2+y^2=64\\y^2=64-(x-2)^2\\y=\sqrt[2]{64-(x-2)^2}[/tex]
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.
