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Question Number 55613 by ajfour last updated on 27/Feb/19

Commented by ajfour last updated on 27/Feb/19

$r e d c u r v e i s y = x^{3} + p x + q$ $b l u e l i n e i s i t s t a n g e n t a t i t s$ $l a r g e s t r o o t .$ $A f t e r r o t a t i o n o f t h e c u r v e$ $a b o u t t h i s r o o t p o i n t P t h e s a m e$ $t a n g e n t i f r o t a t e d t o g e t h e r w i t h$ $t h e c u r v e n o w c o i n c i d e s w i t h t h e$ $x - a x i s . F i n d t h e e q u a t i o n o f t h e$ $n e w c u r v e, h e n c e α .$
Commented by mr W last updated on 28/Feb/19

Commented by mr W last updated on 28/Feb/19

$w h e n t h e c u r v e y = f (x) i s r o t a t e d a b o u t$ $p o i n t P (h, k) b y a n a n g l e θ (+ ↷),$ $t h e n t h e e q n . o f t h e n e w c u r v e i s$ $y_{1} = f (x_{1}) w i t h$ $y_{1} = (x - h) \sin θ + (y - k) \cos θ + k$ $x_{1} = (x - h) \cos θ - (y - k) \sin θ + h$ $o r$ $F (x, y) = (x - h) \sin θ + (y - k) \cos θ + k - f [(x - h) \cos θ - (y - k) \sin θ + h] = 0$
Commented by mr W last updated on 28/Feb/19

Commented by ajfour last updated on 28/Feb/19

$Y e s S i r, t h a n k y o u . I w a s m i s t a k e n$ $i n t h i n k i n g t h a t t h i s t r a n s f o r m a t i o n$ $m i g h t h e l p d e t e r m i n i n g t h e r o o t .$
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