2.Consider Pell's equation associated to n = 2:x² - 2y² = 1.One of the solutions is N(1, 0)(a) Using computer software, plot the curve H defined by the above equation.(b) Find two solutions where x, y > 0 by trial and error. Call them A(x₁, y₁) and B(x2, Y2).(c) Find the equation of the line AB.(d) Find the equation of the line parallel to AB and passing through N. Call this line L.(e) Find the other point of intersection of L and H, call it X (x3, y3). What do you observe?Bonus Express the coordinates of X in term of x1, y1, x2, Y2.

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2. Consider Pell's equation associated to n = 2: x²2y² = = 1. One of the solutions is N(1, 0) (a) Using computer software, plot the curve H defined by the above equation. (b) Find two solutions where x, y> 0 by trial and error. Call them A(x1, y₁) and B(x2, y2). (c) Find the equation of the line AB.

2. Consider Pell's equation associated to n = 2: x²2y² = = 1. One of the solutions is N(1, 0) (a) Using computer software, plot the curve H defined by the above equation. (b) Find two solutions where x, y> 0 by trial and error. Call them A(x1, y₁) and B(x2, y2). (c) Find the equation of the line AB.

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter3: Functions And Graphs

Section3.3: Lines

Problem 22E

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