New Analytic Geometry |
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Common terms and phrases
9 y² a²b² a²y² abscissa asymptotes Ax² axis b²x² bisectors circle coefficients conic conjugate hyperbolas constant construct coördinate axes coördinate planes cos² curve cylinder D₁ determined direction cosines directrix ellipse equal example figure Find the equation Find the locus fixed point foci given equation given line Hence hyperbola hyperboloid intercepts latus rectum length line joining line passing loci middle point negative obtain ordinate origin P₁ P₂ parabola paraboloid parameter parametric equations plane parallel point moves point of intersection polar coördinates PROBLEMS projection quadric radians radius ratio ruled surface satisfy Show sides slope Solution Solving square straight line Substituting surface surface of revolution symmetrical with respect system of lines tangent Theorem triangle whose vertices values variable vertex x-axis x₁ XY-plane Y-axis y₁ YZ-plane Z-axis zero ZX-plane Пх
Popular passages
Page 100 - Plot the locus of a point which moves so that the ratio of its distances from two fixed points remains constant.
Page 66 - 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 100 - A point moves so that the sum of the squares of its distances from the points (0, 0), (1, 0) is constant.
Page 23 - Prove that the middle point of the hypotenuse of a right triangle is equidistant from the three vertices.
Page 188 - Find the locus of a point the sum of the squares of whose distances from two given points is constant.
Page 62 - 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 68 - 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
Page 29 - Show that the area of the triangle whose vertices are (4, 6), (2, —4), (—4, 2) is four times the area of the triangle formed by joining the middle points of the sides.
Page 245 - Thus the locus oí a point at a given distance from a fixed point is a sphere, and the locus of a point equidistant from two fixed points is the plane which is perpendicular to the line joining the given points at its middle point. 2. The locus of a point in space which satisfies two conditions * is, in general...
Page 17 - 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.