Analytic GeometryMacmillan Company, 1910 - 294 páginas |
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Términos y frases comunes
a² b2 abscissa angle approaches the limiting asymptotes Ax approaches ax² Check graphically chord conic constant coördinate axes cos² cycloid direction cosines directrix dx dx dx dy dx ellipse equa equal equations of tangents EXAMPLE EXERCISE Find the equations focus formula function given point Hence hyperbola hypocycloid latus rectum limiting value line parallel locus major axis maximum minimum point negative obtained ordinate origin P₁ P₂ parabola parametric equations perpendicular plane Plot the curves points of intersection polar coördinates positive preceding article primitive curve Prove radian radius ratio rectangular coördinates represents satisfy secant line second derivative curve segment Show sin² slope straight line Substituting surface symmetric with respect tangent line tion triangle variable vertices x-axis x₁ xy-plane y-axis y₁ yz-plane zero
Pasajes populares
Página 106 - The sum of two sides of a triangle is greater than the third side, and their difference is less than the third side.
Página 45 - PF'/PH' = e, by definition of the curve. Furthermore :f (6) PF + PF' = 2a. In fact, the ellipse is often defined as the locus of a point which moves so that the sum of its distances from two fixed points is constant.
Página 92 - A parabola is the locus of a point equally distant from a fixed point and a fixed straight line. The fixed point is called the focus and the fixed straight line the directrix.
Página 65 - The coordinates of the vector in the ox'y' system are (x',y') and, furthermore, as may be verified, x' = x cos 6 + y sin 6 y
Página 166 - The derivative of the quotient of two functions is equal to the denominator times the derivative of the numerator minus the numerator times the derivative of the denominator, all divided by the square of the denominator.
Página 11 - The angle subtended at the center of a circle by an arc equal in length to a radius of the circle.
Página 46 - Plot the locus of a point which moves so that the sum of its distances from two lines at right angles is always 4 inches.
Página 46 - 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.
Página 105 - The difference between two sides of a triangle is less than the third side.
Página 18 - Show that the sum of the projections of the sides of any closed polygon...