## Analytic Geometry |

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### Common terms and phrases

analytically angle asymptotes axes axis becomes bisecting called chord circle circle x² condition conic constant construct converse coördinates corresponding course curve cylinder definition Derive determine diameter direction cosines directrix distance drawn ellipse ends equal evidently Example EXERCISES expressed fact Find the equation Find the tangents foci focus formula geometrically given given point gives Hence hyperbola imaginary infinity joining latus length lies line 3x line x locus means method negative normal obtain origin pairs parabola parallel passing perpendicular plane plot points of intersection positive properties Prove quadratic radius rectum Reduce referred represents respect result roots satisfy second degree segment Show shown slope Solve Ex square standard straight line Substituting surface symmetric tangent term theorem third triangle values variable vertex vertices Write the equation y-axis y₁

### Popular passages

Page 149 - 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 91 - 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 line is called a conic.

Page 63 - A point moves so that the sum of the squares of its distances from two fixed points is constant.

Page 63 - A point moves so that its distances from two fixed points are in a constant ratio k.

Page 60 - A circle is the locus of a point at a constant distance from a fixed point. The fixed point is the center of the circle, and the constant distance is the radius.

Page 10 - N6 is to say that if two nonvertical lines are perpendicular, then the slope of one is the negative reciprocal of the slope of the other.

Page 92 - I, the conic is a parabola; if e > 1, the conic is a hyperbola. Every conic section is representable by an equation of second degree. Conversely, every equation of second degree in two variables represents a conic. Th...

Page 83 - The perpendicular bisectors of the sides of a triangle meet in a point. 12. The bisectors of the angles of a triangle meet in a point. 13. The tangents to a circle from an external point are equal. 14...

Page 31 - A point moves so that the sum of its distances from the two axes is always equal to 10.

Page 63 - Find the locus of a point which moves so that the square of its distance from the base of an isosceles triangle is equal to the rectangle under its distances from the other sides.