(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.

Algebra and Trigonometry (MindTap Course List)

4th Edition

ISBN:9781305071742

Author:James Stewart, Lothar Redlin, Saleem Watson

Publisher:James Stewart, Lothar Redlin, Saleem Watson

Chapter12: Conic Sections

Section12.5: Rotation Of Axes

Problem 1E: Suppose the x- and y-axes are routed through an acute angle to produce the new X- and Y-axes. A...

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