By Lewis Parker Siceloff, George Wentworth and David Eugene Smith

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Extra info for Analytic geometry

Sample text

22. The rod AB in the figure is 4ft. long, has a knob (P) 1ft. from A, and slides with its ends on OX and OY respectively. Find the equation of the locus of P. From the conditions of the problem P moves so that OK: KA = 3 : 1. y B 23. In Ex. ~~A>:--x= draw the locus. 24. -2 0(0, 0) with a force equal to 10/ OP, and towards A (12, 0) with a force equal to 5j AP 2 , find the equation of the locus of all points P which are equally attracted towards 0 and A, and draw this locus. 25. If a certain spiral spring 6 in.

The notation a ~ x ~ b means that x is equal to or greater than a, and is equal to or less than b ; that is, it means that x may have any value in the interval from a to b, inclusive of a and b. The notation a< x < b means that x may have any value in the interval from a to b, exclusive of a and b. In examining a quadratic equation for the purpose of determining the intervals of values of x for which y is real, we are often aided by solving the equation for y in terms of x, factoring expressions under radicals if possible.

P (a, b), given that OP = 5 and the slope of OP is 2. • 32 GEOMETRIC MAGNITUDES 61. Given that AP = PB, AP is perpendicular to PB, A is (2, 3), and B is (- 3, - 2), find the coordinates of P. 62. The mid point of the hypotenuse of a right triangle is equidistant from the three vertices. This theorem, familiar from elementary geometry, makes no mention of axes. ·we, therefore, choose the most convenient axes, which, in this case, are those which lie along OA and OB. From the coordinates of A (a, 0) and of B(O, b), we can find those of M and the three distances referred to in the exercise.