A Companion to Wrigley's Collection of Examples: Being Illustrations of Mathematical Processes and Methods of Solution |
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Page 200
... curve coincides with the axis of x ; and the concavity of the parabola is towards the negative direction of x . 4 . y2 + 2xy + x2 + y − 3x + 1 = 0 . To take away the term involving xy , let Then xt cos - u sin 0 , y = t sin ◊ + u cos ...
... curve coincides with the axis of x ; and the concavity of the parabola is towards the negative direction of x . 4 . y2 + 2xy + x2 + y − 3x + 1 = 0 . To take away the term involving xy , let Then xt cos - u sin 0 , y = t sin ◊ + u cos ...
Page 202
... curves ; if therefore y1 , ya , be the ordinates on the upper side of the axis , and -y ,, -y , the ordinates on the ... curve y2 = 4αx , a is y = = mx + where m = tan 0 , " m and the equation to the tangent to the circle is y = mx + c ...
... curves ; if therefore y1 , ya , be the ordinates on the upper side of the axis , and -y ,, -y , the ordinates on the ... curve y2 = 4αx , a is y = = mx + where m = tan 0 , " m and the equation to the tangent to the circle is y = mx + c ...
Page 207
... curves , the values of x and y in equations ( 1 ) and ( 2 ) must be the same , therefore , eliminating y , we have x { h + k + 2 ( xh ) 3 sin — w } − 2 { k ( h ) * + h ( k ) * sin 1 w } - + h { k - c cot - c cot / w } = = 0 , 2 and ...
... curves , the values of x and y in equations ( 1 ) and ( 2 ) must be the same , therefore , eliminating y , we have x { h + k + 2 ( xh ) 3 sin — w } − 2 { k ( h ) * + h ( k ) * sin 1 w } - + h { k - c cot - c cot / w } = = 0 , 2 and ...
Page 211
... curve when the origin of co - ordinates is removed to the centre , becomes 3x2 + 2x'y ' + y'3 — 2 = 0 . Turning the axes through an angle 0 , and equating to zero the coefficient of xy , we get − 6 sin 0 cos 0 + 2 ( cos2 0 — sin2 0 ) + ...
... curve when the origin of co - ordinates is removed to the centre , becomes 3x2 + 2x'y ' + y'3 — 2 = 0 . Turning the axes through an angle 0 , and equating to zero the coefficient of xy , we get − 6 sin 0 cos 0 + 2 ( cos2 0 — sin2 0 ) + ...
Page 212
... curve then becomes - 16x'2 + 7y'2 + 16x'y ' — 36 = 0 ........ .. ( 1 ) . Now transfer the axis of y through an angle of 30 ° , and we have ' : = 2y " √3 ' x ' = x " y " - √3 which values being substituted in ( 1 ) , we have for the ...
... curve then becomes - 16x'2 + 7y'2 + 16x'y ' — 36 = 0 ........ .. ( 1 ) . Now transfer the axis of y through an angle of 30 ° , and we have ' : = 2y " √3 ' x ' = x " y " - √3 which values being substituted in ( 1 ) , we have for the ...
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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