Consider the two circles a(t) = (cos(t), sin(t)), B(t) = (2+2 cos(t), 1+2 sin(t)). where t e [0, 27]. In this problem, we will show that the two circles meet at a right-angle at the point Q, as in the below diagram. -34 25 15 05 15 -1 -0.5 10 0.5 1.5 2.5 3.5 4.5 -0.5 (a) Your friend Tonga is trying to find the exact Cartesian coordinates of Q. But she ends up proving that the two circles never actually intersect. Here is her argument: To find the intersection points, we set a(t) = B(t) and solve for t. This results in two equations: cos(t) = 2+2 cos(t) and sin(t) = 1+2 sin(t). But the first equation is equivalent to cos(t) = -2, which has no solution! This means that there is no value of t for which a(t) = B(t), which means that the two circles never intersect. What's wrong with Tonga's argument? 2,

Consider the two circles a(t) = (cos(t), sin(t)), B(t) = (2+2 cos(t), 1+2 sin(t)). where t e [0, 27]. In this problem, we will show that the two circles meet at a right-angle at the point Q, as in the below diagram. -34 25 15 05 15 -1 -0.5 10 0.5 1.5 2.5 3.5 4.5 -0.5 (a) Your friend Tonga is trying to find the exact Cartesian coordinates of Q. But she ends up proving that the two circles never actually intersect. Here is her argument: To find the intersection points, we set a(t) = B(t) and solve for t. This results in two equations: cos(t) = 2+2 cos(t) and sin(t) = 1+2 sin(t). But the first equation is equivalent to cos(t) = -2, which has no solution! This means that there is no value of t for which a(t) = B(t), which means that the two circles never intersect. What's wrong with Tonga's argument? 2,

Intermediate Algebra

10th Edition

ISBN:9781285195728

Author:Jerome E. Kaufmann, Karen L. Schwitters

Publisher:Jerome E. Kaufmann, Karen L. Schwitters

Chapter8: Conic Sections

Section8.2: More Parabolas And Some Circles

Problem 63.1PS

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