Answer
$(0, 0)$
$(3, \sqrt 3)$
$(3, -\sqrt 3)$
Work Step by Step
Given the system of equations:
1. $x^2 + y^2 = 4x$
2. $x = y^2$
It asks to find all solutions.
Substitute $x = y^2$
$x^2 + x = 4x$
$x^2 - 3x = 0$
$x (x-3) = 0$
$x = 0, 3$
Substitute the values into the equation
$0^2 + y^2 = 4(0)$
$y = 0$
$3^2 + y^2 = 4(3)$
$y^2 = 3 $
$y = +/- \sqrt 3$
All solutions:
$(0, 0)$
$(3, \sqrt 3)$
$(3, -\sqrt 3)$
