Analytic Geometry, a First Course |
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algebraic analytic geometry angle arbitrary asymptotes ax² axes of co-ordinates axis of symmetry bisected By² central conic coefficients condition of tangency conjugate diameters conjugate hyperbola corresponding curve deduce definition denote determined directrix ellipse equa equal evidently Find the equation Find the intersections Find the locus finite fixed point foci focus given line harmonic conjugate hyperbola imaginary points infinite discontinuities July July 13 length line at infinity loci method necessary and sufficient negative number of points ordinates origin P₁ pair of conjugate pairs of values parabola paragraph parallel parameters perpendicular plane plotting point of intersection position problem radius real points reduce the equation represented respect secant line second degree Show slope straight line student sub-tangent substitution sufficient condition tangent and normal tends to zero theorem tion tracing point variable point Write the equation x₁ y₁
Popular passages
Page 33 - A point moves so that the sum of the squares of its distances from the points (0, 0), (1, 0) is constant.
Page 86 - A conic is the locus of a point whose distance from a fixed point called the focus is in a constant ratio to its distance from a fixed line called a directrix.
Page 141 - Thus ike modulus of the product of two complex numbers is the product of their moduli, and the argument of the product is the sum of their arguments.
Page 86 - Tofind the locus of a point, the difference of whose distances from two fixed points is always equal to a given quantity 2 a.
Page 23 - ... therefore as having the same intensity as the direct light (screened as above) when viewed from the same distance ; but with a continuous curve surface, such as a parabolic reflector, we must consider the divergency of the emanating ray at the point where it falls on the reflector, which will vary inversely as the square of the distance of that point from the centre of the light, or directly as the square of the sine of half the angle which the light subtends from that point, and therefore as...
Page 104 - In the chapter on polar coordinates we find the one time familiar definition of a conic as " the locus of a point moving in such a way that its distance from a fixed point is proportional to its distance from a fixed straight line.
Page 99 - Prove that the area of the parallelogram formed by the tangents at the extremities of two conjugate diameters of an ellipse is constant, and is equal to 4 ab.
Page 137 - The length of the projection of a limited line upon any other line, is equal to the length of the line multiplied by the cosine of the angle between them.
Page 86 - The locus of a point which moves so that its distance from a fixed point _ its distance from a fixed line (where e is a constant greater than 1), is called a hyperbola.