The discussion focuses on finding the y-coordinates of the intersection points between the circle defined by the equation x² + y² - 10x + 2y + 17 = 0 and the y-axis. By substituting x = 0 into the equation, the resulting quadratic equation y² + 2y + 17 = 0 is derived. The solutions to this quadratic will determine the y-coordinates of the intersection points, if any exist. Additionally, understanding the circle's center and radius from previous problems can simplify this process.
PREREQUISITESStudents studying algebra, geometry enthusiasts, and educators teaching coordinate geometry concepts will benefit from this discussion.
If a point lies on the $y$-axis then its $x$-coordinate is $0$. If you put $x=0$ in the equation of the circle then it becomes $y^2 + 2y + 17 = 0.$ The solutions of that quadratic (if there are any) will give you the points (if any) where the circle intersects the y-axis.RTCNTC said:Find the y-coordinates of the points (if any) where the circle intersects the y-axis.
x^2 + y^2 - 10x + 2y + 17 = 0
Can someone share the steps with me?
Opalg said:If a point lies on the $y$-axis then its $x$-coordinate is $0$. If you put $x=0$ in the equation of the circle then it becomes $y^2 + 2y + 17 = 0.$ The solutions of that quadratic (if there are any) will give you the points (if any) where the circle intersects the y-axis.
However, if you have previously solved your other problem about this circle (where you had to find its centre and radius), you may find that that gives you a simpler way to answer this problem.