MHB Find y-coordinates of the Points

  • Thread starter Thread starter mathdad
  • Start date Start date
  • Tags Tags
    Points
Click For Summary
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.
mathdad
Messages
1,280
Reaction score
0
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?
 
Mathematics news on Phys.org
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.
 

Thread 'Area of Overlapping Squares'

Here is a little puzzle from the book 100 Geometric Games by Pierre Berloquin. The side of a small square is one meter long and the side of a larger square one and a half meters long. One vertex of the large square is at the center of the small square. The side of the large square cuts two sides of the small square into one- third parts and two-thirds parts. What is the area where the squares overlap?
View full post »

Similar threads

High School Invariant under rotation: Banal, obvious, or noteworthy?
  • · Replies 2 ·
Replies
2
Views
2K
MHB What are the coordinates of points equidistant from (1,0) and (5,4)?
  • · Replies 6 ·
Replies
6
Views
1K
MHB [ASK] A Line Intercepting A Circle
  • · Replies 4 ·
Replies
4
Views
1K
MHB Find Center and Radius of Circle
  • · Replies 2 ·
Replies
2
Views
2K
Undergrad My attempt to understand horizontal transformations of functions
  • · Replies 6 ·
Replies
6
Views
2K
MHB Finding 2D Polygon Coordinates from a point
  • · Replies 2 ·
Replies
2
Views
2K
MHB How Are Tangents to a Circle Found and Their Intersection Point Determined?
  • · Replies 5 ·
Replies
5
Views
2K
MHB What is the Center and Radius of a Circle?
  • · Replies 9 ·
Replies
9
Views
2K
MHB Finding Points of Intersection for Trigonometric Functions
  • · Replies 8 ·
Replies
8
Views
3K
Undergrad Transforming coordinates between Cartesian and spherical
  • · Replies 1 ·
Replies
1
Views
2K