Analytical Geometry (the Straight Line and Circle). |
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Common terms and phrases
apply F Ax+By+C ax² axis of x bisectors bisects chord of contact circle whose centre circle x² coincident points condition cos a+y sin curve cuts the axes Data fixing diameter directrix distance dx+ey ellipse equa equations simultaneously factors Find the co-ordinates Find the equation Find the length Find the lines Find the locus find the point fixed points formula geometrical given point hyperbola intercept latus rectum line joining line whose equation lines parallel lines represented loci method of Art numerical parabola parallel to OX perpendicular point of contact point which moves point x1 points of intersection positive quadratic radical axis radius rectangular co-ordinates reference required equation right angles Show sides square straight line substitute Tangent or polar three lines tion triangle values vertex Write the equation y=mx y=mx+c y₁ y²+dx+ey+f=0 y²=c² zero
Popular passages
Page 61 - 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 62 - A point moves so that the sum of the squares of its distances from the points (0, 0), (1, 0) is constant.
Page 70 - The parabola may also be defined as the locus of a point whose distance from a fixed point ( the focus) is equal to its distance from a fixed straight line (the directrix), ie its eccentricity (qv) is 1. From this definition its construction readily follows. Let DD
Page 64 - 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 71 - 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 71 - Anthemius was familiar with the focus-directrix property of a conic. (The locus of a point whose distance from a fixed point bears a constant relation to its...
Page 65 - Show that the locus of a point from which the tangents to two...
Page 65 - The locus of points whose distances from two fixed points have a given ratio (m :n) is the circumference of a circle whose diameter divides the line joining the fixed points harmonically in the given ratio. Prove : I. That any point in the circumference satisfies the given condition. II. That any point satisfying the given condition lies in the circumference. I.
Page 64 - The locus of a point whose distances from two fixed points are in a constant ratio (not one of equality) is a circle.
Page 61 - Hence the radical axis of two circles is perpendicular to the line joining their centres. @/ The three radical axes of three circles taken in pairs meet in a point. If S = 0, S' = 0, S" = 0 be the equations of three circles (in each of which the coefficient of a?