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a-axis according acē angle asymptotes axes axis becomes called centre changed CHAPTER chord circle coefficients coincident condition cone conic constant coordinates corresponding curve derivative determine difference direction directrix distance Draw drawn ellipse equal EXAMPLES expressed figure Find the equation Find the locus foci focus four function Geometry given gives Hence hyperbola imaginary integral length limit line joining loci locus maximum meet method moves negative normal obtained opposite origin pair parabola parallel passing perpendicular plane point of intersection pole positive Prove radius ratio rectangular referred represents respect result roots satisfy Show sides slope sphere square standard straight line Substituting surface symmetrical tangent touch Transform triangle values variable varies vertices written y-axis z-axis zero
Pāgina 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.
Pāgina 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.
Pāgina 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.
Pāgina 131 - The locus of the middle points of a system of parallel chords in a parabola is called a diameter.
Pāgina 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.
Pāgina 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.
Pāgina 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.
Pāgina 184 - The locus of a point, the sum of the squares of whose distances from n fixed points is constant, is a circle.