Analytic Geometry |
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Common terms and phrases
algebraic asymptotes axis b₁ called Completing the squares Consequently constant coördinate axes coördinate planes coördinates satisfy cos² cylinder determine direction cosines distance ellipse equa equal equation x² equivalent Example Exercises expression factors Find its equation Find the equation Find the locus find the point Find the polar fixed circle fixed point function given graph Hence hyperbola initial line length middle point nates negative origin P₁P2 P₂ pairs parabola parametric equations passes perpendicular PIP2 Plot the curve polar coördinates polar equation polynomial projections quantities radius real number rectangular coördinates rectangular equation represents root satisfy the equation second degree segment semi-axes Show side simultaneous equations slope solutions solved straight line surface symmetrical with respect tangent tion triangle variable vector vertex vertices x-axis xy-plane y-axis y₁ yz-plane z-axis zero
Popular passages
Page 87 - A point moves so that the sum of the squares of its distances from the points (0, 0), (1, 0) is constant.
Page 87 - A point moves so that the square of its distance from the point (0, 3) equals the cube of its distance from the axis of y.
Page 126 - A curve defined as the locus of a point which moves so that the product of its distances from two fixed points is constant and equal to the square of half the distance between the fixed points.
Page 75 - The parabola is the locus of a point which moves so that its distance from a fixed point is equal to its distance from a fixed line.
Page 87 - Any curve which is the locus of a point which moves so that the ratio of its distance from a fixed point to its distance from a fixed line is constant.
Page 72 - Plot the locus of points the sum of whose distances from two fixed points remains constant.
Page 81 - Find the locus of a point the difference of whose distances from two given parallel lines is equal to a given length.
Page 29 - In an inscribed quadrilateral, the product of the diagonals is equal to the sum of the products of the opposite sides.
Page 155 - That is, the sum of the squares of the direction cosines of a line is unity.