Analytic Geometry |
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Common terms and phrases
a² b2 a²m² algebraic asymptotes bisecting bisector conic conjugate diameters conjugate hyperbola coördinate axes coördinate planes corresponding values determine directed segment direction cosines directrix Discuss the equation distance Draw the graph eccentricity ellipse equa example Find the coördinates Find the equation Find the lengths fixed point focal radii foci focus given equation Hence hyperbola hypocycloid initial line intercepts inverse function latus rectum line joining loci locus locus is symmetrical monotone function negative origin P₁ P₂ pair parabola parallel parametric equations perpendicular plot point moves point of contact points whose coördinates polar coördinates polar equation polar line pole preceding article quadrant r₁ radical axis rectangular coördinates represents semiaxes Show slope standard form straight line surface symmetrical with respect tangent THEOREM tion transverse axis vertex Write the equation X-axis x₁ Y-axis Y-intercepts y₁
Popular passages
Page 57 - A point moves so that the sum of the squares of its distances from the points (0, 0), (1, 0) is constant.
Page 60 - 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.
Page 125 - The locus of the middle points of a system of parallel chords in a parabola is called a diameter.
Page 175 - The curve traced by a fixed point on the circumference of a circle as the circle rolls in a plane along a fixed straight line is called the cycloid.
Page 206 - The lines drawn from each vertex of a tetrahedron to the point of intersection of the medians of the opposite face all meet in a point called the...
Page 63 - 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 62 - As defined, the term e is the ratio of the distance between the foci to the length of the major axis.
Page 101 - Find the equation of the line which passes through the intersection of the lines 2 x — 3y + 1 =0 and x + 5?/ + 6=0 and is perpendicular to the first of these lines.
Page 181 - ... equation of the locus of the foot of the perpendicular from the pole on to any tangent to the curve.
Page 50 - Boyle's law. The volume of a gas is inversely proportional to the pressure if the temperature remains constant.