35. The cissoids r = a sin 0 tan 0. (See Exercise 29.) Ans. sin 0 cos 0 dr - r(1+ cos? 0) d0 = 0.
35. The cissoids r = a sin 0 tan 0. (See Exercise 29.) Ans. sin 0 cos 0 dr - r(1+ cos? 0) d0 = 0.
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter11: Topics From Analytic Geometry
Section11.4: Plane Curves And Parametric Equations
Problem 20E
Related questions
Question
Kindly answer item 35. Show your complete solution.
![|Ch. 1
16
Definitions, Families of Curves
31. Circles through the intersections of the circle x2 + y? = 1 and the line y = x.
Use the "u + kv" form; that is, the equation
%3D
x? + y2 - 1+ k(y – x) = 0.
Ans. (x2 - 2xy – y² + 1) dx + (x²+ 2xy- y2-1) dy = 0.
32. Circles through the fixed points (a, 0) and (-a, 0). Use the method of Exercise
Ans. 2xy dx + (y² + a? – x?) dy = 0.
31.
-cos 0).
Ans. (cos 0- sin 0) dr + r(cos 0+ sin 0) d0 = 0.
33. The circles r =
2a(sin 0
Ans. (1 sin 0) dr +r cos 0 d0 = 0.
34. The cardioids r = a(1- sin 0).
35. The cissoids r = a sin 0 tan 0. (See Exercise 29.)
Ans. sin 0 cos e dr - r(1 + cos? 0) de = 0.
dr
= r sec 0.
de
36. The strophoids r =
a(sec 0+ tan 0).
Ans.
37. The trisectrices of Maclaurin r =
a(4 cos 0- sec 0). (See Exercise 30.)
cos 0(4 cos? 6 - 1) dr +r sin (4 cos? 0 + 1) d60 = 0.
Ans.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F1823a70a-58c1-4f1d-bd4c-d04cac8ed9ab%2F2def60a9-adc3-4479-a616-01d3f9c9ea4d%2Fp0eso6_processed.jpeg&w=3840&q=75)
Transcribed Image Text:|Ch. 1
16
Definitions, Families of Curves
31. Circles through the intersections of the circle x2 + y? = 1 and the line y = x.
Use the "u + kv" form; that is, the equation
%3D
x? + y2 - 1+ k(y – x) = 0.
Ans. (x2 - 2xy – y² + 1) dx + (x²+ 2xy- y2-1) dy = 0.
32. Circles through the fixed points (a, 0) and (-a, 0). Use the method of Exercise
Ans. 2xy dx + (y² + a? – x?) dy = 0.
31.
-cos 0).
Ans. (cos 0- sin 0) dr + r(cos 0+ sin 0) d0 = 0.
33. The circles r =
2a(sin 0
Ans. (1 sin 0) dr +r cos 0 d0 = 0.
34. The cardioids r = a(1- sin 0).
35. The cissoids r = a sin 0 tan 0. (See Exercise 29.)
Ans. sin 0 cos e dr - r(1 + cos? 0) de = 0.
dr
= r sec 0.
de
36. The strophoids r =
a(sec 0+ tan 0).
Ans.
37. The trisectrices of Maclaurin r =
a(4 cos 0- sec 0). (See Exercise 30.)
cos 0(4 cos? 6 - 1) dr +r sin (4 cos? 0 + 1) d60 = 0.
Ans.
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