The Principles of Analytical Geometry, Part 1 |
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Page 3
... cosw . - 2 - = If the axes be rectangular , that is , if wπ the above becomes PQ2 = ( x2 − x1 ) 2 + ( Y2 — Y1 ) 2 . ― - 6. We have seen that in order to fix the position of a point in a plane we have two separate elements or quantities ...
... cosw . - 2 - = If the axes be rectangular , that is , if wπ the above becomes PQ2 = ( x2 − x1 ) 2 + ( Y2 — Y1 ) 2 . ― - 6. We have seen that in order to fix the position of a point in a plane we have two separate elements or quantities ...
Page 31
... cosw m sin w 1 + m cos w therefore tanα = therefore tan ( a — a ' ) - = ( m - m ' ) sin w 1+ ( m + m ' ) cosa + mm ' " which is the tangent of the angle between the two lines . If the lines are perpendicular to each other , we must have ...
... cosw m sin w 1 + m cos w therefore tanα = therefore tan ( a — a ' ) - = ( m - m ' ) sin w 1+ ( m + m ' ) cosa + mm ' " which is the tangent of the angle between the two lines . If the lines are perpendicular to each other , we must have ...
Page 35
... cosw , the axes being inclined at an angle w . 10. Find the length of the perpendicular from the point ( a , 0 ) on the straight line , whose equation is X y + α b C = ( a2 + b2 ) * 11. Find the equation to the line passing through the ...
... cosw , the axes being inclined at an angle w . 10. Find the length of the perpendicular from the point ( a , 0 ) on the straight line , whose equation is X y + α b C = ( a2 + b2 ) * 11. Find the equation to the line passing through the ...
Page 43
... cosw = r2 , - x2 + y2 + 2xy cosw - 2 ( a + b cosa ) x - 2 ( b + a cosa ) y + a + b2 + 2ab cosw = r2 , and therefore the equation x2 + y2 + Axy + Bx + Cy + D = 0 represents a circle when the axes are inclined to each other at an angle o ...
... cosw = r2 , - x2 + y2 + 2xy cosw - 2 ( a + b cosa ) x - 2 ( b + a cosa ) y + a + b2 + 2ab cosw = r2 , and therefore the equation x2 + y2 + Axy + Bx + Cy + D = 0 represents a circle when the axes are inclined to each other at an angle o ...
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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