## Analytic Geometry |

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### Common terms and phrases

abscissa angle asymptotes axes axis b²x² called chords circle x² common conic consider constant coordinates corresponding curve cuts Denote determined directrix distance divide Draw Draw the graph eccentricity ellipse equal evident example Exercise figure Find the equation fixed foci focus geometry given graph Hence hyperbola intercepts intersection length limit locate locus major means meet method mid point moves negative normal origin pair parabola parabola y² parallel passes perpendicular plane plot polar positive PROBLEM produced Proof prove quadrant radius ratio rectangular referred represents respect result roots satisfy segment Show sides slope Solution square straight line student surface symmetric tangent THEOREM tion trace triangle units values vertex vertices write written x₁ y₁

### Popular passages

Page 38 - A conic section is the locus of a point which moves so that its distance from a fixed point, called the focus, is in a constant ratio to its distance from a fixed straight line, called the directrix.

Page 106 - A point moves so that the sum of the squares of its distances from the four sides of a square is constant.

Page 32 - Prove that the middle point of the hypotenuse of a right triangle is equidistant from the three vertices.

Page 115 - 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 223 - The cycloid is a plane curve formed by a point on a circle as the circle rolls along a straight line.

Page 145 - 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 106 - Find the equation of the circle inscribed in the triangle formed by the lines x + y = 0, x - 7y + 24 = 0, and 7x - y -8 = 0.

Page 138 - Prove that the ordinate of the point of intersection of two tangents to a parabola is the arithmetical mean between the ordinates of the points of contact of the tangents.

Page 87 - Find the equations of the bisectors of the angles formed by the lines ox - 12 y+ 10 = 0 and 12x - by + 15 = 0.

Page 240 - POx{ , are called the direction angles of the line, and their cosines are called direction cosines.