Analytic Geometry |
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Common terms and phrases
a² b2 a²b² a²y² abscissa analytic geometry angle asymptotes ax² axes b²x² by² called circle with center circle x² common points conic conjugate diameters conjugate hyperbola constant contours curve cycloid Denote direction cosines directrix draw the figure Draw the graph eccentricity ellipse equa equal equation x² equidistant Exercise find the coordinates Find the equation Find the locus Find the point find the value focal width foci focus Hence increases without limit intercepts intersection length locate locus major axis mid point negative normal ordinate origin P₁ pair parabola y² parallel to OX parametric equations passes perpendicular point h point P(x polar coordinates positive PROBLEM quadrant radians radical axis radius ratio Show Solution straight line surface symmetric with respect tangent THEOREM tion triangle vertex vertices x₁ x²/a² y₁ y²/b²
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 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 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 106 - A point moves so that the sum of the squares of its distances from the four sides of a square is constant.
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 240 - ... y, z respectively. These angles are called the direction angles of the line, and their cosines are called the direction cosines of the line.
Page 223 - The cycloid is a plane curve formed by a point on a circle as the circle rolls along a straight line.
Page 216 - 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 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 182 - The equation of the locus of the foot of the perpendicular from the center of...