Analytic Geometry |
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Common terms and phrases
abscissa analytic geometry angle asymptotes Ax² bisects By² called chord circle x² conic conjugate conjugate hyperbola constant Construct coordinate axes corresponding cos² curve cuts the X-axis DEFINITION derive the equation diameter directrix distance ellipse equa equal Find the coordinates Find the equation Find the lengths foci focus geometry given points graph Hence hyperbola latus rectum line joining loci locus negative ordinate origin P₁ P₂ pairs parabola parallel to YOZ parameter parametric equations passes perpendicular plane parallel point of intersection point x1 polar axis polar coordinates positive radius real lines real point represents respectively result semi-axes side slope straight line Substituting surface tangent THEOREM tion transformation values variables vertex X-axis x₁ x²/a² Y-axis y-intercept y₁ y²/b² zero
Popular passages
Page 14 - The line joining the mid-points of two sides of a triangle is parallel to the third side, and equal to half the third side.
Page 65 - ... distance from a fixed point. The fixed point is called the center of the circle, and the constant distance is called the radius.
Page 129 - The tangent at any point of a parabola makes equal angles with the axis and the focal distance of the point.
Page 63 - Prove analytically that the perpendicular bisectors of the sides of a triangle meet in a point.
Page 21 - For every value of x there are two equal values of y with opposite signs.
Page 75 - 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 74 - Find the equation of the locus of a point whose distance from the z-axis is twice its distance from the xy-plane.
Page 39 - A point moves so that the sum of its distances from the two points (0, V5), (0, -VB) is always equal to 8.
Page 63 - Find the equation of the line which passes through the point of intersection of the lines.
Page 36 - A point moves so that the sum of the squares of its distances from two fixed points is constant. Prove that the locus is a circle.