Analytic Geometry |
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Common terms and phrases
a²b² a²y² abscissa analytic geometry angle asymptotes Ax² axes 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 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 lemniscate of Bernoulli 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 point Q polar coordinates positive PROBLEM Proof 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 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.