Analytic Geometry |
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Common terms and phrases
9 x² 9 y² angle asymptotes Ax² axis is parallel bisectors bisects called chord circle x² Completing the squares conic conic section conjugate conjugate hyperbola constant coördinate axes coördinate planes cos² determined diameter directrix ellipse equa equal EXERCISES figure Find the coördinates Find the equation foci focus formula hyperbola ILLUSTRATIVE EXAMPLE intercepts latus rectum line joining loci major axis nates ordinate origin parametric equations passes perpendicular Plot the locus point moves point P₁ point which moves polar axis polar coördinates pole positive principal axis Proof Prove radical axis rectangular coördinates represents rotation satisfy the equation second degree semi-minor axis sets of axes sides slope Solving standard equation straight line Substituting subtangent surface symmetrical with respect tangent tion transverse axis values variable vertex Whence Write the equation x-axis y-axis y-intercept y₁
Popular passages
Page 220 - Find the equation of the locus of a point which moves so that the sum of the squares of its distances from the x- and z-axes equals 4.
Page 128 - 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 110 - 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 132 - 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 120 - An ellipse is the locus of a point which moves so that the ratio of its distance from a fixed point, called the focus, to its distance from a fixed line, called the directrix, is constant and less than unity.
Page 220 - PF'/PH' = e, by definition of the curve. Furthermore :f (6) PF + PF' = 2a. In fact, the ellipse is often defined as the locus of a point which moves so that the sum of its distances from two fixed points is constant.
Page 109 - A point moves so that the sum of the squares of its distances from the four sides of a square is constant.
Page 138 - PF'/PH'= e, by the definition of the curve. Furthermore :J (b) \PF—PF'\=2a. In fact, the hyperbola is often defined as the locus of a point which moves so that the difference of its distances from two fixed points is constant.
Page 209 - Hyperbola is the locus of a point which moves so that its distance from a fixed point, called the focus, bears a constant ratio, which is greater than unity, to its distance from a fixed straight line, called the directrix.
Page 109 - 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.