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Prove that the equation S =x+4xy+3y²– 4x – 10y +3=0 represents a pair of lines and find the equations of the lines.

Prove that the equation S =x+4xy+3y²– 4x – 10y +3=0 represents a pair of lines and find the equations of the lines.

Advanced Engineering Mathematics
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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Question
Example 2.24 Prove that the equation S =x² + 4xy + 3y² – 4x – 10y + 3 = 0 represents a pair of lines and find the equations of the lines. THEOREM 2.33 Suppose that the straight line Ix + my = 1 meets the curve represented by the second-degree gen- eral equation S = ax² + 2hxy + by² + 2gx + 2fy+c = 0 at two points A and B. If O is the origin, then the combined equation of the pair of lines OA and OB is S' = ax? + 2hxy + by² +2(gx+ fy)(lx + my)+c(lx+my)² = 0
Transcribed Image Text:Example 2.24 Prove that the equation S =x² + 4xy + 3y² – 4x – 10y + 3 = 0 represents a pair of lines and find the equations of the lines. THEOREM 2.33 Suppose that the straight line Ix + my = 1 meets the curve represented by the second-degree gen- eral equation S = ax² + 2hxy + by² + 2gx + 2fy+c = 0 at two points A and B. If O is the origin, then the combined equation of the pair of lines OA and OB is S' = ax? + 2hxy + by² +2(gx+ fy)(lx + my)+c(lx+my)² = 0
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