A Companion to Wrigley's Collection of Examples: Being Illustrations of Mathematical Processes and Methods of Solution |
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Page 205
... locus , which is an hyperbola , whose eccentricity = sec I α . 2 29. Let ẞ be the constant angle between the tangent ... locus of ( 1 ) and ( 2 ) , for these values do not satisfy both ( 1 ) and ( 2 ) , hence the re- quired locus is y ...
... locus , which is an hyperbola , whose eccentricity = sec I α . 2 29. Let ẞ be the constant angle between the tangent ... locus of ( 1 ) and ( 2 ) , for these values do not satisfy both ( 1 ) and ( 2 ) , hence the re- quired locus is y ...
Page 206
... ) = 0 , - for the equation to the locus which is an ellipse , whose minor axis ( coincident with the axis of the parabola ) is h , and major axis is h√√2 . 41. The equations to the parabola and circle referred to 206 PARABOLA .
... ) = 0 , - for the equation to the locus which is an ellipse , whose minor axis ( coincident with the axis of the parabola ) is h , and major axis is h√√2 . 41. The equations to the parabola and circle referred to 206 PARABOLA .
Page 210
... locus of C is a parabola . = ELLIPSE . Ex . 4 . 2C I + cos 0 ; 1. 3 3 ( x2 - 2 x + 1 ) I = I + + 2 ( y2 + y + 1 ) · + 16 8 2 y + + 35 = 24 35 72 3 35 48 Hence the co - ordinates of the centre of ellipse , are h = ' 313 , k the semi ...
... locus of C is a parabola . = ELLIPSE . Ex . 4 . 2C I + cos 0 ; 1. 3 3 ( x2 - 2 x + 1 ) I = I + + 2 ( y2 + y + 1 ) · + 16 8 2 y + + 35 = 24 35 72 3 35 48 Hence the co - ordinates of the centre of ellipse , are h = ' 313 , k the semi ...
Page 215
... locus ( y2 — b3 ) = c ( x2 — a2 ) , - - which , c being a negative quantity , represents an ellipse whose centre is the centre of the given ellipse . 33. Let O be the centre of the circle , △ PCT = 0 , ≤OCT = ß . Draw CD parallel to ...
... locus ( y2 — b3 ) = c ( x2 — a2 ) , - - which , c being a negative quantity , represents an ellipse whose centre is the centre of the given ellipse . 33. Let O be the centre of the circle , △ PCT = 0 , ≤OCT = ß . Draw CD parallel to ...
Page 217
... locus - y2 – ky , x2 + b2 - hx = 0 , a2 ka La ha = a2 ba + ( 2y - k ) , ( 2x - h ) 2 or + b2 which is therefore an ellipse , the co - ordinates of whose centre are B212 h k and 2 and whose semi - axes are 26 ( a2k2 + b2h2 ) * and I 2a ...
... locus - y2 – ky , x2 + b2 - hx = 0 , a2 ka La ha = a2 ba + ( 2y - k ) , ( 2x - h ) 2 or + b2 which is therefore an ellipse , the co - ordinates of whose centre are B212 h k and 2 and whose semi - axes are 26 ( a2k2 + b2h2 ) * and I 2a ...
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A Companion to Wrigley's Collection of Examples: Being Illustrations of ... John Thompson Platts,Alfred Wrigley No preview available - 2016 |
Common terms and phrases
a+b+c a²+b² a²b³ AB² ABCD AC² angle ABC axis BC² beam centre of gravity chord circle co-ordinates coefficient cos² cos³ cosec² curve diameter draw ellipse equal equilateral Eucl Hence hyperbola Join latus rectum Let ABC middle point MULTINOMIAL THEOREMS parabola parallel perpendicular plane point of contact point of intersection r₁ radius required locus right angle roots S₁ sec² segment sides Similarly sin² sin³ square straight line tan² tangent term transformed equation triangle ABC values vertical weight whence X₁