The Principles of Analytical Geometry, Part 1 |
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Page 47
... touching the circle at the point x'y ' , eliminating x and y ' from this equation , by means of the following : and 12 x ' y = my 12 x " + y'2 = r2 , we have , for the equation of the required line , y = mx ± r √ ( 1 + m3 ) . Hence ...
... touching the circle at the point x'y ' , eliminating x and y ' from this equation , by means of the following : and 12 x ' y = my 12 x " + y'2 = r2 , we have , for the equation of the required line , y = mx ± r √ ( 1 + m3 ) . Hence ...
Page 53
... touch each other , the radical axis becomes the common tangent , for it passes through the point of con- tact , and is perpendicular to the line joining their centres . If the circles ... circle . The polar equation to the circle THE CIRCLE .
... touch each other , the radical axis becomes the common tangent , for it passes through the point of con- tact , and is perpendicular to the line joining their centres . If the circles ... circle . The polar equation to the circle THE CIRCLE .
Page 55
... of intersection of the line 2 x y = + -1 , α b 2 with the circle x2 + y2 = r2 , and deduce the condition that must hold in order that the line may touch the circle . 10. Find the equation to a line touching the circle THE CIRCLE . 55.
... of intersection of the line 2 x y = + -1 , α b 2 with the circle x2 + y2 = r2 , and deduce the condition that must hold in order that the line may touch the circle . 10. Find the equation to a line touching the circle THE CIRCLE . 55.
Page 56
10. Find the equation to a line touching the circle ( x − a ) 2 + ( y — b ) 2 = r2 , - and parallel to a given line . 11. Find the radius and centre of the circle x2 + y2 - 6x + 4y + 4 = 0 . 12. Find the equation to the straight line ...
10. Find the equation to a line touching the circle ( x − a ) 2 + ( y — b ) 2 = r2 , - and parallel to a given line . 11. Find the radius and centre of the circle x2 + y2 - 6x + 4y + 4 = 0 . 12. Find the equation to the straight line ...
Page 57
... touching the circle x2 + y2 = 10 at points , the common abscissa of which is unity . 27. Find the equation to a line touching a given circle ( x − a ) 2 + ( y — b ) 2 = r2 , and ... circles represented by the equation ( THE CIRCLE .. 57.
... touching the circle x2 + y2 = 10 at points , the common abscissa of which is unity . 27. Find the equation to a line touching a given circle ( x − a ) 2 + ( y — b ) 2 = r2 , and ... circles represented by the equation ( THE CIRCLE .. 57.
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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