MHB Find y-coordinates of the Points

[mathdad]

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]

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?

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.

 

[mathdad]

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.

Good to know that part A of this problem also yields an answer to part B.