An Elementary Course in Analytic Geometry |
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Common terms and phrases
abscissa algebraic Analytic Geometry asymptotes Ax² axis bisects By² chord of contact circle x² conic section conjugate diameters conjugate hyperbola constant coördinate axes curve directrix drawn eccentricity ellipse equa equal EXERCISES Find the equation Find the locus find the points fixed point foci focus formulas geometric given circle given equation given line given point hence hyperbola initial line latus rectum length loci locus of equation M₁ method middle point ordinate origin P₂ pair parabola y² parallel perpendicular point of contact point of intersection point P₁ point which moves polar coördinates polar equation pole positive radius represents satisfy secant secant line secant method 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 Y₂
Popular passages
Page 234 - Find the locus of the center of a circle which passes through a given point and touches a given line.
Page 105 - ... by the square root of the sum of the squares of the coefficients of x...
Page 106 - 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 168 - 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 118 - 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 177 - 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 238 - 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 21 - The projection of a point upon a line is the foot of the perpendicular from the point to the line.
Page 120 - 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 209 - 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.