(b) In each of the following situations find a formula describing the locus of the point P, in Cartesian coordinates, and briefly describe the shape of the locus. (It is not necessary to give detailed geometric properties of the shape such as its centre.) (i) The distance from P₁ to the point (-2,2) is equal to that from P₁ to (0,4). (ii) The distance from P₂ to the point (1,3) is twice that from P₂ to (-1,2). (iii) The distance from P3 to the line 3y = 4x is 1. (iv) The distance from P4 to the point (-5,3) is twice the distance from P4 to the line with equation 4x + 3y + 5 = 0.
(b) In each of the following situations find a formula describing the locus of the point P, in Cartesian coordinates, and briefly describe the shape of the locus. (It is not necessary to give detailed geometric properties of the shape such as its centre.) (i) The distance from P₁ to the point (-2,2) is equal to that from P₁ to (0,4). (ii) The distance from P₂ to the point (1,3) is twice that from P₂ to (-1,2). (iii) The distance from P3 to the line 3y = 4x is 1. (iv) The distance from P4 to the point (-5,3) is twice the distance from P4 to the line with equation 4x + 3y + 5 = 0.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
question B
Transcribed Image Text:2. (a) Let L be a set of points in the plane. Consider the following statement S:
"If L is described by the equation y = mx + c for some m, c E R, then L is a
straight line."
(i) Is S true?
(ii) Write down the converse of S.
(iii) Is the converse of S true?
Briefly explain your answers.
(b) In each of the following situations find a formula describing the locus of the point
P₁ in Cartesian coordinates, and briefly describe the shape of the locus. (It is not
necessary to give detailed geometric properties of the shape such as its centre.)
(i) The distance from P₁ to the point (-2,2) is equal to that from P₁ to (0,4).
(ii) The distance from P₂ to the point (1,3) is twice that from P₂ to (-1,2).
(iii) The distance from P3 to the line 3y = 4x is 1.
(iv) The distance from P4 to the point (-5,3) is twice the distance from ₁ to
the line with equation 4x + 3y + 5 = 0.
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 4 steps with 4 images
Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
