Introduction to Analytic Geometry |
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Introduction to Analytic Geometry Percey Franklyn Smith,Arthur Sullivan Gale No preview available - 2015 |
Common terms and phrases
a²b² abscissa algebraic Analytic Geometry angle asymptotes Ax² bisectors coefficients conic conic section conjugate hyperbolas constant term coördinate planes Corollary curve Cy² directed line directrix distance ellipse Find the area Find the coördinates Find the equation foci following equations Fourth step given equation given line Hence hyperbola intercepts latus rectum line joining line parallel line passing loci middle points negative obtain origin P₁ P₁P P₁P₂ P₂ parabola perpendicular Plot the locus point of intersection point P1 polar axis polar coördinates positive direction problem projection Proof quadratic quadrics Radians radical axis radius real numbers rectangular coördinates required equation right triangle roots satisfy second degree Second step Show sides slope Solution Solving straight line Substituting symmetrical with respect tangent Theorem Third step triangle whose vertices values variables vertex X-axis x₁ XY-plane Y-axis y₁
Popular passages
Page 90 - The line joining the middle points of two sides of a triangle is parallel to the third side and equal to half of the third side.
Page 59 - A point moves so that the sum of the squares of its distances from the points (0, 0), (1, 0) is constant.
Page 58 - Find the equation of the locus of a point which moves so that its distances from (8, 0) and (2, 0) are always in a constant ratio equal to 2.
Page 59 - In the proofs of the following theorems the choice of the axes of coordinates is left to the student, since no mention is made of either coordinates or equations in the problem. In such cases always choose the axes in the most convenient manner possible.
Page 58 - The locus of a point, the sum of the squares of whose distances from n fixed points is constant, is a circle.
Page 34 - Prove that the middle point of the hypotenuse of a right triangle is equidistant from the three vertices.
Page 202 - Ex. 1. Find the equation of the locus of a point whose distance from Pi(3, 0, -2) is 4.
Page 78 - N6 is to say that if two nonvertical lines are perpendicular, then the slope of one is the negative reciprocal of the slope of the other.
Page 58 - A point moves so that the difference of the squares of its distances from two fixed points is constant. Show that the locus is a straight line. Hint. Draw XX' through the fixed points, and YY/ through their middle point.
Page 22 - The projection of a point upon a line is the foot of the perpendicular from the point to the line. 329. DEF. The projection of one line upon another is the segment between the projections of the extremities of the first line upon the second. A' / ri U/ A A B' A