## An Elementary Course in Analytic Geometry |

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### Common terms and phrases

abscissa analytic angle axes axis becomes called CHAPTER chord circle coincident condition conic constant Construct coördinate axes coördinates corresponding curve cuts definition derived determined diameter direction directrix distance draw drawn ellipse equa equal example EXERCISES Express figure Find the equation fixed point focus formulas function geometric given point gives hence hyperbola joining known length loci locus means meet method moves normal Note obtained origin P₁ pair parabola parallel passes perpendicular plane points of intersection polar pole positive projection properties Prove radius ratio rectangular reduces referred regard relation represents respectively roots satisfy Show shown side slope Solve square straight line Substituting taken tangent tion trace transformation triangle values variables vertex vertices written x-axis y-axis y₁

### Popular passages

Page 104 - 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 220 - Find the locus of the center of a circle which passes through a given point and touches a given line.

Page 92 - 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 154 - 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 163 - 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 403 - The laboratory work is adapted to any equipment, and ihe instructions for it are placed in divisions by themselves, preceding the related chapters of descriptive text, which follows in the main the order of topics in Gray's Lessons in Botany. Special attention is paid to the ecological aspects of plant life, while at the same time morphology and physiology are fully treated. There are 384 carefully drawn illustrations, many of them entirely new.

Page 224 - 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 106 - 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 195 - 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 81 - A point moves so that the difference of the squares of its distances from two fixed points is constant. Show that the locus is a straight line. Hint. Draw XX' through the fixed points, and YY/ through their middle point.