Question

why is y²=x²-x⁴ <=> y= +/- x*sqrt(1-x²) ? what's the step I'm missing?

Answer 1

what I don't see is how x comes out of the square root

Answer 2

\[\sqrt{x^2-x^4}=\sqrt{x^2(1-x^2)}=\sqrt{x^2}\sqrt{1-x^2}=x\sqrt{1-x^2}\] assuming x is positive

Answer 3

ok thanks

Answer 4

\[1-x ^{2}\ge 0,1 \ge x ^{2} ,or x ^{2} \le 1,-1 \le x \le 1 ,y=\pm x \sqrt{1-x ^{2}}\]