An Analytical System of Conic Sections: Designed for the Use of Students |
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Common terms and phrases
a² a² a² b² a² sin² a² y² a²² a²b² a²yy abscissa axes axes of co-ordinates axis AX b2 a² b² cos² b²x² b²x²² b²xx bisect centre circle Conic Section conjugate diameters conjugate hyperbola curve cut the axis denote directrix distance draw e²x² ellipse equal equation a² equation required fall the perpendicular find the equation find the locus focus given in position given point Hence hyperbola indeterminate equation joining the points latus rectum let fall line joining major axis meeting the ellipse middle points negative oblique ordinate pairs of tangents parabola parallel to AX point of intersection points of contact polar equation rectangle contained rectangular right angles semi-minor axis shewn ß² substitution subtangent supplemental chords supposed tangent theory of equations values vertex x²²
Popular passages
Page 40 - Straight line and circle. A straight line cannot cut a circle in more than two points. In fact, an unlimited straight line may (i) cut a circle in two points, eg AB or CD in fig.
Page 142 - AB describe a segment of a circle containing an angle equal to the given angle, (in.
Page 189 - Fig. 83,84. conjugate diameters is equal to the sum of the squares of the axes ; but in an hyperbola the difference of the squares of any two conjugate diameters is equal to the difference of the squares of the axes.
Page 59 - A conic section is the locus of a point whose distances from a fixed point and a fixed line are in a constant ratio. 4. Show that every conic is represented by an equation of the second degree in x and y. Hint. Take Y Y' to coincide with the fixed line, and draw XX
Page 39 - When it is affirmed (for instance) that " if two straight lines in a circle intersect each other, the rectangle contained by the segments of the one is equal to the rectangle contained by the segments of the other...
Page 174 - In any equation in its simplest form the coefficient of the second term is equal to the sum of the roots with their signs changed ; the coefficient of the third term is equal to the sum of the products of every two...
Page 79 - Hence if from the several points of any straight line pairs of tangents be drawn to an ellipse, the straight lines which join the corresponding points of contact will all pass through the same point.