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Read or Download Plane and Solid Analytic Geometry: An Elementary Textbook PDF
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Extra info for Plane and Solid Analytic Geometry: An Elementary Textbook
Sample text
With MN be given in 45 B^y -f 0, ^» in Art. 2 = - ;g^* tane^^g^^Af Hence [11, 5] PROBLEMS 1. T'ind the angle the line x-\-2y Solution. which the — The angle is to ——^. / makes with MX in Fig. 32. last line, Hence h and that ^^^ =h Substituting these values in [11, a], tan 6 = i^ = e = tan-i 13. or line X a; be measured from the line therefore takes the place of 1-2 line 5 = l. / = 10, . tan d = ~^~^ = - 13, ^ = tan-i(- 1-f 13). i =—| ANALYTIC GEOMETRY 46 Find the angle which the 2. with the line 11 Find the 3.
The and 0) (a, Then the coor- two points are 0). We can translate into an algebraic equa- tion the statement that a point P, coordinates equally fixed distant points (x^ y), from shall be the two and A^ by ex- pressing the distances of JP from each of the two points, and equating these two expressions. In Fig. 22, Ch. 23 LOCI Ill, § 15] ^ve have, as the Squaring and reducing, equation of the desired locus, a " Here the ment of the law. algebraic result is, does not express so clearly as in the final result previous cases that = 2- is it But simply a translation of the stateit has been obtained by simple reductions from this statement.
The here, student and lowing demonstrations, himself that the assure proof should in all the fol- is perfectly general. Place the lines and points in different positions, being careful to give the same letter and the demonstrations ought to For example, try Fig. 28 with the to corresponding points, hold, letter for letter. above demonstration, being careful to note that P^L =31,0 -{- = OAT - 031 031^, LP = L3I + 3IP = 3IP - 3IL, P,K= 31,0 + 031,^ = OM,^ - 031,, KP, = K3I,^ -f 3I,P^ Equation [5] may be written X y = 3I,P,^ in the 1 0.