An Elementary Treatise on Conic Sections and Algebraic Geometry: With Numerous Examples and Hints for Their Solution. Especially Designed for the Use of Beginners ... |
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An Elementary Treatise on Conic Sections and Algebraic Geometry: With ... George Hale Puckle No preview available - 2016 |
An Elementary Treatise on Conic Sections and Algebraic Geometry: With ... George Hale Puckle No preview available - 2016 |
Common terms and phrases
2Hxy asymptotes Ax² axes being rectangular axis axis of x By² centre chord of contact circle x² coefficients coincident coincident points condition conic section conjugate diameters conjugate hyperbola constant cos² directrix ellipse equa equal equation Art equation becomes find the equation find the locus focus four points given point Hence the equation hyperbola imaginary inclined infinite distance intercepts latus rectum Let the equation meet the curve middle point negative obtain ordinates pair parabola perpendicular point x'y points of contact points of intersection polar equation pole positive quantity ratio represents two straight right angles roots satisfy second degree shew shewn Similarly sin² straight line drawn straight line joining straight line passing suppose tangent tion touch triangle of reference values vertex written
Popular passages
Page 24 - ... by the square root of the sum of the squares of the coefficients of x and y.
Page 143 - Prove algebraically that the angles in the same segment of a circle are equal, and that the angle in a semicircle is a right angle.
Page 92 - ... the first is to the third as the difference between the first and second is to the difference between the second and third, the quantities a, b, c, are said to be in harmonical proportion.
Page 45 - Find the equation to the straight line which passes through the points (2, 5) and (0, - 7). 3. The co-ordinates of the angular points of a triangle being given, find the equations to the three straight lines, each of which bisects two of the sides. 4. Two straight lines make each of them an angle of 45...
Page 237 - The radius of the circle, which touches an hyperbola and its asymptotes, is equal to that part of the latus rectum produced which is intercepted between the curve and the asymptote.
Page 256 - To find the polar equation to the parabola, the focus being the pole.
Page 363 - We learn that the locus of a point, such that the tangent from it to a fixed circle is in a constant ratio to its distance from a fixed line...
Page 56 - To find the area of a triangle in terms of the coordinates of the angular points, the axes being rectangular.
Page 46 - Determine the poiut of intersection of the two lines (3?/ -x = 0) and (2x + y = 1). 7. Find the equation to the straight line which passes through the point of intersection of the straight lines x - 2y - a = 0, x + 3y — 2a = 0, and is parallel to the line Zx + 4y = 0.
Page 240 - The locus of the middle points of a system of parallel chords in a parabola is called a diameter.