1. Consider a circle of radius 6 with center at the origin. a. Lines with slopes 1 and -1 each intersect the circle in two points. Find the coordinates of these points. b. If you know one of the points of intersection in Part a, how can you use the symmetry of the circle to determine the remaining three? √3 c. The line y = ." 3 x intersects the circle in two points. Find the coordinates of those points. Find the coordinates of the points on the circle that are sym- metric to these points with respect to the x-axis. Then find the equation of the line containing these new points. V3 d. What angle does y = x make with the x-axis? 3
1. Consider a circle of radius 6 with center at the origin. a. Lines with slopes 1 and -1 each intersect the circle in two points. Find the coordinates of these points. b. If you know one of the points of intersection in Part a, how can you use the symmetry of the circle to determine the remaining three? √3 c. The line y = ." 3 x intersects the circle in two points. Find the coordinates of those points. Find the coordinates of the points on the circle that are sym- metric to these points with respect to the x-axis. Then find the equation of the line containing these new points. V3 d. What angle does y = x make with the x-axis? 3
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:### Analytical Geometry Problem Set
#### Problem 1:
Consider a circle of radius 6 with center at the origin.
**a.** Lines with slopes 1 and -1 each intersect the circle in two points. Find the coordinates of these points.
**b.** If you know one of the points of intersection in Part a, how can you use the symmetry of the circle to determine the remaining three?
**c.** The line \( y = \frac{\sqrt{3}}{3} x \) intersects the circle in two points. Find the coordinates of those points. Find the coordinates of the points on the circle that are symmetric to these points with respect to the x-axis. Then find the equation of the line containing these new points.
**d.** What angle does \( y = \frac{\sqrt{3}}{3} x \) make with the x-axis?
This problem set focuses on the application of geometric principles to the circle, involving line intersections, symmetry, and angular relationships.
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