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 conic section conjugate diameters conjugate hyperbola constant coördinate axes cos² curve directrix 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 length limaçon line joining loci locus of equation M₁ method middle point nates normal ordinate origin P₁ and P2 P₂ pair parabola y² perpendicular point P₁ points of intersection polar coördinates polar equation pole positive radius ratio rectangular coördinates represents satisfy 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 y₂
Popular passages
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 234 - Find the locus of the center of a circle which passes through a given point and touches a given line.
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 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 65 - 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 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 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.
Page 167 - 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.