An Elementary Course in Analytic Geometry |
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Common terms and phrases
abscissa Analytic Geometry angle asymptotes Ax² axis bisects By² chord of contact circle x² conic section conjugate diameters conjugate hyperbola constant coördinate axes coördinate planes cos² curve directrix draw eccentricity ellipse equa equal EXERCISES find the coördinates Find the equation Find the locus fixed point foci focus formulas geometric given equation given line given point hence hyperbola initial line latus rectum line joining loci locus of equation M₁ method middle point normal ordinate origin P₁ P₂ pair parabola parallel perpendicular point P₁ point which moves points of intersection polar coördinates polar equation pole positive radius ratio represents satisfy secant line second degree shows side slope standard form straight line subtangent tangent tion trace transformation triangle VA² values variables vertex vertices Write the equation x-axis x₁ y-axis y-intercept y₁
Popular passages
Page 102 - 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 218 - Find the locus of the center of a circle which passes through a given point and touches a given line.
Page 90 - 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 152 - 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 161 - 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 401 - 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 222 - 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 104 - 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 193 - 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 79 - 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.