An Elementary Course in Analytic Geometry |
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Common terms and phrases
abscissa Analytic Geometry asymptotes Ax² axis bisects By² chord of contact circle x² conic section conjugate diameters conjugate hyperbola constant coördinate axes curve directrix eccentricity ellipse equa equal EXAMPLES ON CHAPTER EXERCISES Find the equation Find the locus fixed point foci focus formulas geometric given circle given equation given line given point hence hyperbola initial line latus rectum length line joining loci locus of equation M₁ method middle point normal ordinate origin P₂ pair parabola y² parallel perpendicular point of contact point P₁ point which moves points of intersection polar coördinates polar equation pole positive radical axis radius represents satisfy secant secant line second degree Show side slope standard form straight line subtangent tangent tion traced transformation triangle values variables vertex vertices Write the equation x-axis x₁ y-axis y-intercept y₁
Popular passages
Page 120 - The straight line joining the middle points of two sides of a triangle is parallel to the third side, and equal to half of it.
Page 108 - 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 236 - To find the locus of the centre of a circle which passes through a given point and touches a given straight line.
Page 179 - F') ; the diameter drawn through them is called the major axis, and the perpendicular bisector of this diameter the minor axis. It is also defined as the locus of a point which moves so that the ratio of its distance from a fixed point...
Page 67 - A conic section or conic is the locus of a point which moves so that its distance from a fixed point is in a constant ratio to its distance from a fixed straight line...
Page 240 - Art. 144 is sometimes given as the definition of the ellipse ; viz. the ellipse is the locus of a point the sum of whose distances from two fixed points is constant.
Page 122 - The line joining the middle points of two sides of a triangle is parallel to the third side and equal to half of the third side.
Page 211 - To draw that diameter of a given circle which shall pass at a given distance from a given point. 9. Find the locus of the middle points of any system of parallel chords in a circle.
Page 169 - A point moves so that the square of its distance from the base of an isosceles triangle is equal to the product of its distances from the other two sides.
Page 108 - A plane curve which Is the locus of a point which moves so that it is at a constant distance (the radius) from a fixed point (the centre).