Brief Course in Analytic Geometry |
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Common terms and phrases
a² b2 abscissa Analytic Geometry analytically asymptotes Ax² By² circle x² conic section conjugate diameters conjugate hyperbola constant coördinate axes coördinate planes cos² curve directrix drawn eccentricity ellipse equa equal EXERCISES Find the equation Find the locus fixed point focal radii foci focus geometry given equation given line given point hence hyperboloid initial line latus rectum length line parallel loci M₁ major axis middle point numbers ordinate origin P₂ parabola y² passes perpendicular point of contact point P₁ points of intersection polar coördinates polar equation radical axis radius rectangular axes rectangular coördinates represents secant secant line secant method second degree semi-axes Show slope standard equation standard form straight line subnormal subtangent surface tangent and normal trace transformation transverse axis triangle values variables vertex vertices Write the equations x-axis x-intercept x₁ y-axis y₁
Popular passages
Page 194 - To find the locus of the centre of a circle which passes through a given point and touches a given straight line.
Page 84 - 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 35 - Prove that the points (a, b + c), (b, c + a), and (c, a + 6) lie on the samp straight line. (cf. Ex. 2, p. 37.) CHAPTER III THE LOCUS OF AN EQUATION 32. The locus of an equation. A pair of numbers x, y is represented geometrically by a point in a plane. If these two numbers (x, y) are variables, but connected by an equation, then this equation can, in general, be satisfied by an infinite number of pairs of values of x and y, and each pair may be represented by a point. These points will not, however,...
Page 144 - CON'IC, OR CONIC SECTION, n. 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 137 - 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 88 - The straight line joining the middle points of two sides of a triangle is parallel to the third side, and equal to half of it.
Page 153 - 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 179 - To draw that diameter of a given circle which shall pass at a given distance from a given point. 9. Find the locus of the middle points of any system of parallel chords in a circle.
Page 114 - A point moves so that the square of its distance from the base of an isosceles triangle is equal to the product of its distances from the other two sides. Show that the locus is a circle. 50. Prove that the two circles z2 + y2 + 2 G,z + 2 Ftf + Cj = 0 and x2 + y...
Page 57 - A point moves so that the difference of the squares of its distances from (3, 0) and (0, — 2) is always equal to 8.