The Principles of Analytical Geometry, Part 1 |
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Page 48
... chord joining the two points of contact of tangents through an external point ( x'y ' ) . Let P be the given point x'y ' , O the centre of the given circle , and let PQ and PT be the tangents through PTQ the line whose equation is ...
... chord joining the two points of contact of tangents through an external point ( x'y ' ) . Let P be the given point x'y ' , O the centre of the given circle , and let PQ and PT be the tangents through PTQ the line whose equation is ...
Page 49
... chord of contact will be xx ' + yy ' = r2 , for this is the equation to a straight line , and it has been shewn that the points of contact lie on it , since their coordi- nates satisfy it . 50. A chord of a circle is drawn through a ...
... chord of contact will be xx ' + yy ' = r2 , for this is the equation to a straight line , and it has been shewn that the points of contact lie on it , since their coordi- nates satisfy it . 50. A chord of a circle is drawn through a ...
Page 50
... contact joined , these lines all pass through one point . Let Ax + By + C = 0 be the given line , and x'y ' any point in it . Then the equation to the chord of contact of tangents through this point will be xx ' + yy ' = r2 . But since ...
... contact joined , these lines all pass through one point . Let Ax + By + C = 0 be the given line , and x'y ' any point in it . Then the equation to the chord of contact of tangents through this point will be xx ' + yy ' = r2 . But since ...
Page 51
... chords of contact all pass through a given point which can be determined by the above formulæ . Let y - mx = 0 be the equation to a line passing through the centre of the circle , and let it be required to find the point in which the chords ...
... chords of contact all pass through a given point which can be determined by the above formulæ . Let y - mx = 0 be the equation to a line passing through the centre of the circle , and let it be required to find the point in which the chords ...
Other editions - View all
The Principles of Analytical Geometry: Designed for the Use of Students Henry Parr Hamilton No preview available - 2016 |
Common terms and phrases
ANALYTICAL GEOMETRY angle POX axes being inclined axes being rectangular axis of x bisecting the angle centre Chapter chord of contact circle x² Conic Sections cosa+y cosw Crown 8vo cuts the circle denotes the distance diameter Differential Calculus equal equation becomes equation x² evidently ex recensione Find the coordinates Find the equation Find the length Find the locus fixed point x'y given circle given line Greek HYPERIDES initial line line cutting line joining line OX line represented line ST line whose equation lines are parallel middle points origin of coordinates P₁ perpendicular point of intersection points whose coordinates polar coordinates polar equation PQ² radical axis radius referred required equation Second Edition Shew siny Ox straight line passing substituting tangent Third Edition touching the circle triangle Trinity College University of Cambridge values x²²