Analytic Geometry |
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Common terms and phrases
abscissa ANALYTIC GEOMETRY asymptotes ax² axis parallel Bisecting chords cartesian coördinates central conic chord of contact circle x² conic section conic x² constant contact corresponding coördinate planes cylinder determine diameter directing curve direction cosines directrix Draw the figure ellipse Example Find the equation Find the locus find the points Find the tangents fixed point foci formula geometrically given line given point Hence hyperbola imaginary latus rectum line 3x line x method ordinates origin P₁ parabola y² parallel to Ox passing perpendicular point moves points at infinity points of intersection points P1 positive quadratic quadric radical axis radius vector represents rotation of axes second degree segment slope Solve Ex straight line Substituting surface symmetric with respect term theorem of Ex touches the line trace the curve transverse axis values vertex vertices Write the equation x-axis y-axis y-intercept 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.