MHB Find y-coordinates of the Points

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To find the y-coordinates where the circle intersects the y-axis, substitute x=0 into the circle's equation, resulting in the quadratic y^2 + 2y + 17 = 0. Solving this quadratic will reveal any intersection points. It is noted that if the circle's center and radius were previously determined, this information could simplify the process. The discussion emphasizes that understanding part A of the problem can aid in solving part B effectively.
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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?
 
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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?
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.
 
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.

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

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