Elementary Mathematical Analysis |
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algebraic analytic geometry angle ax² axes B₁ C₁ called change ratio circle coefficients complex numbers conic constant cos² cosines curve degree determinant directed segments directrix distance Draw the graph ellipse equa equal EXAMPLE EXERCISES expression factor figure Find the coördinates Find the equation Find the value formula geometric given Hence hyperbola increases integer intersection length locus logarithms multiply negative nth roots obtain origin P₁ P₂ parabola parallel parametric equations perpendicular plane polar coördinates polynomial positive Prove quadrant quadratic function radians radius real number relation represents result roots scale Show sides sin² sine slide rule slope solution Solve square straight line tangent temperature theorem tion triangle trigonometric functions variable vector vertex vertices x-axis x₁ y-axis y-intercept y₁ zero
Popular passages
Page 323 - Show that the locus of a point which moves so that the sum of its distances from two h'xed straight lines is constant is a straight line.
Page 324 - Find the equation of the locus of a point which moves so that its distances from (8, 0) and (2, 0) are always in a constant ratio equal to 2.
Page 440 - The modulus of the product of two complex numbers is equal to the product of their moduli.
Page 424 - The number of combinations of n different things taken r at a time is equal to the number of permutations of n different things, taken r at a time, divided by r!.
Page 424 - Recall the general formula for the number of combinations of n different things taken r at a time, C(n,r) n\ r!(nr)!
Page 209 - Hence the Law of Tangents : The difference of two sides of a triangle is to their sum as the tangent of half the difference of the opposite angles is to the tangent of half their sum. NOTE.
Page 353 - PH' the perpendiculars from P to the directrices; then (a) PF/PH = e and PF'/PH'= e, by the definition of the curve. Furthermore :J (b) \PF—PF'\=2a. In fact, the hyperbola is often defined as the locus of a point which moves so that the difference of its distances from two fixed points is constant.
Page 337 - A conic section is the locus of a point which moves so that its distance from a fixed point, called the focus, is in a constant ratio to its distance from a fixed straight line, called the directrix.
Page 122 - Quadratic equations may be put into the form ax2 + bx + c = 0, where a, b, and c are constants and a =£ 0.
Page 228 - I. The characteristic of any number greater than 1 is one less than the number of digits before the decimal point. The following table, which is taken from § 1, p.