The Elements of Plane and Solid Analytic Geometry |
Other editions - View all
Common terms and phrases
a² b2 angle asymptotes axes axis bisected called centre chords circle x² coefficients coincident cone conic sections conicoid conjugate diameters conjugate hyperbolas constant coordinate planes corresponding cos² curve direction cosines directrix distance ellipse equal EXAMPLES Find the equation Find the locus fixed point foci Geometry given equation given points Hence hyperbola hyperboloid imaginary latus rectum Let P(x Let the equation line joining line passing loci maximum meet middle points negative ordinate origin P₁ pair of values parabola parallel perpendicular Plane Geometry points of intersection polar coordinates polar equation positive radical axis radius real roots rectangle represents required equation root of f(x satisfy Show sides sin² slope sphere square standard form straight line surface symmetrical with respect variable vertex vertices x-axis x-intercepts y-axis y₁ zero
Popular passages
Page 41 - Find the locus of a point, the distances of which from two given straight lines have a fixed ratio. 143. Find the locus of a point which moves so that the sum of its distances from two vertices of an equilateral triangle shall equal its distance from the third.
Page 17 - The sum of the squares of the four sides of any quadrilateral is equal to the sum of the squares of the diagonals plus four times the square of the line joining the mid-points of the diagonals.
Page 38 - 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 184 - Find the locus of a point such that the sum of the squares of its distances from two fixed points shall be equivalent to the square of the distance between the fixed points.
Page 131 - The locus of the middle points of a system of parallel chords in a parabola is called a diameter.
Page 130 - Shew that the locus of the middle points of a system of parallel chords of a parabola is a straight line parallel to the axis of the parabola.
Page 40 - 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 108 - Norman window consists of a rectangle surmounted by a semicircle. If the perimeter of the window is given, what must be its proportions in order to admit as much light as possible ? Ans.
Page 184 - The locus of a point, the sum of the squares of whose distances from n fixed points is constant, is a circle.
Page 107 - A = 2 try? -\ • x 10. An open box is to be made from a sheet of pasteboard 12 in. square, by cutting equal squares from the four corners and bending up the sides. Plot the volume V as a function of the side x of the square cut out.