1. Let l be the line of the extended Euclidean plane through the points P (1,2,3) and Q = (1,1,1), and let C be the conic in the extended Euclidean plane given by the equation 3r + y? - 22 +2yz- 2xz- 2ry 0. (a) Find the coordinates of l. (b) Rewrite the equation of C in the form X'AX = 0, where A is a symmetric matrix. (c) Show thatP C. (d) Use Joachmisthal's equation to find the other point of intersection of I and C. (e) What type of conic results if C is restricted to the Euclidean plane?
1. Let l be the line of the extended Euclidean plane through the points P (1,2,3) and Q = (1,1,1), and let C be the conic in the extended Euclidean plane given by the equation 3r + y? - 22 +2yz- 2xz- 2ry 0. (a) Find the coordinates of l. (b) Rewrite the equation of C in the form X'AX = 0, where A is a symmetric matrix. (c) Show thatP C. (d) Use Joachmisthal's equation to find the other point of intersection of I and C. (e) What type of conic results if C is restricted to the Euclidean plane?
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter5: Orthogonality
Section5.5: Applications
Problem 49EQ
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