## An Elementary Course in Analytic Geometry |

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### Common terms and phrases

abscissa analytic angle asymptotes axes axis becomes called CHAPTER chord circle circle x2 coincident condition conic conjugate constant Construct coördinate axes coördinates corresponding curve definition derived determined diameter direction directrix distance draw drawn eccentricity ellipse equa equal example EXERCISES expressed figure Find the equation focus formulas function geometric given point gives hence hyperbola length loci locus meet method moves normal NOTE obtained origin P₁ pair parabola parallel passes perpendicular plane points of intersection polar pole positive properties Prove radius ratio rectangular reduces referred regard relation represents respectively result satisfy Show shown side slope solving square standard form straight line Substituting surface tangent tion traced transformation triangle values variables vertex vertices written x-axis y-axis

### 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 236 - Find the locus of the center of a circle which passes through a given point and touches a given line.

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 170 - Thus a parabola is the locus of a point which moves so that its distance from a fixed point is equal to its distance from a fixed straight line (see fig.

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.