Analytic Geometry |
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Common terms and phrases
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 Denote direction cosines directrix draw the figure Draw the graph eccentricity ellipse equa equation x² equidistant Exercise find the coordinates Find the equation Find the locus Find the point find the slope find the value focal width foci focus Hence increases without limit intersection length line parallel locus major axis mid point negative normal ordinate origin P₁ pair parabola y² parallel to OX parametric equations perpendicular point P(x polar coordinates positive PROBLEM Proof quadrant radians radical axis radius ratio Show Solution square straight line student subtangent surface symmetric with respect tangent THEOREM tion triangle vertex vertices x₁ x²/a² y₁ y²/b²
Popular passages
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 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 223 - The locus of a point on a circle as the circle rolls along a straight line is called a cycloid.
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 192 - Find the locus of the center of a circle which is tangent to a fixed circle and a fixed 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 43 - Two points are said to be symmetric with respect to a line if the line is the perpendicular bisector of the line segment which joins the two points.
Page 240 - Denote by a, 0, 7 the angles which a directed line makes with the positive directions of the axes of x, y, z respectively. These angles are called the direction angles of the line, and their cosines are called the direction cosines of the line.