The base of triangle passes through a fixed point p(a,b) and its sides are respectively bisected at right angles by the line x+y=0 and x=9y if the locus of the third vartex is a circle. then find its equation.


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Question Number 43005 by mondodotto@gmail.com last updated on 06/Sep/18

$The base of triangle passes through$ $a fixed point p (a, b) and its sides$ $are respectively bisected at right angles$ $by the line x + y = 0 and x = 9 y$ $if the locus of the third vartex is a circle .$ $then find its equation .$
Commented by mondodotto@gmail.com last updated on 06/Sep/18

$please help me this problem$
Commented by ajfour last updated on 06/Sep/18

Commented by ajfour last updated on 06/Sep/18

$l e t A (h, k)$ $\Rightarrow B (- k, - h)$ $l e t C (α, β)$ $r e f l e c t i o n o f C i n y = m x + c i s$ $α = h - \frac{2 m (c + m h - k)}{1 + m^{2}}$ $β = k + \frac{2 (c + m h - k)}{1 + m^{2}}$ $h e r e w e h a v e y = \frac{x}{9}$ $\Rightarrow m = \frac{1}{9}, c = 0$ $\Rightarrow α = h - \frac{\frac{2}{9} (\frac{h}{9} - k)}{1 + \frac{1}{81}}$ $\Rightarrow α = h - \frac{9}{41} (\frac{h}{9} - k)$ $a n d β = k + \frac{81}{41} (\frac{h}{9} - k)$ $e q . o f l i n e t h r o u g h B C i s$ $y + h = \frac{β + h}{α + k} (x + k)$ $A s t h i s p a s s e s t h r o u g h P (a, b)$ $b + h = \frac{β + h}{α + k} (a + k)$ $r e p l a c i n g α, β i n t e r m s o f h, k$ $a n d c h a n g i n g h, k t o x, y w e g e t$ $t h e d e s i r e d l o c u s o f A (t h i r d v e r t e x)$ $b + h = \frac{k + \frac{81}{41} (\frac{h}{9} - k) + h}{h - \frac{9}{41} (\frac{h}{9} - k) + k} (a + k)$ $\Rightarrow (b + x) [x + y - \frac{9}{41} (\frac{x}{9} - y)]$ $= (a + y) [x + y + \frac{81}{41} (\frac{x}{9} - y)]$ $l o c u s f o u n d i s$ $40 (x^{2} + y^{2}) - 41 (b - a) (x + y)$ $- 9 (a x - b y) = 0 .$
Commented by tanmay.chaudhury50@gmail.com last updated on 06/Sep/18

$d e a r a j f o u r s i r w h i c h a p p h e l p s t o d r a w . . . f o r$ $e x a m p l e t h i s p r o b l e m . . .$
Commented by ajfour last updated on 06/Sep/18

$l e k h d i a g r a m .$ $i h a v e u n d e r s t o o d h o w t o u s e i t$ $a n y c o n f u s i o n, u c a n a s k m e . .$
Commented by tanmay.chaudhury50@gmail.com last updated on 06/Sep/18

$o k t h a n k y o u . . . i h a v e l a t e n t w i s h t o s e e o u r s e l v e s$ $w e a r e v i r t u a l l y c o n n e c t e d b u t n e v e r s e e e a c h o t h e r$ $s o i f a d m i n o f t h i s a p p g i v e p e r m i s s i o n t o u p l o a d$ $o u r p i c t u r e a t l e a s t o n e c e . . . i$
Commented by MJS last updated on 06/Sep/18

$we could upload a self portrait including a$ $math example . . .$
Commented by mondodotto@gmail.com last updated on 06/Sep/18

$thanx$
Commented by tanmay.chaudhury50@gmail.com last updated on 06/Sep/18

Commented by tanmay.chaudhury50@gmail.com last updated on 06/Sep/18

Commented by behi83417@gmail.com last updated on 06/Sep/18

$w o n d e r f u l i d e a!$ $w a i t i n g f o r s i r : M r W 3, a j f o u r,$ $s i r M J S, p r o p . A b d o, . . . . .$
Commented by MJS last updated on 06/Sep/18

Commented by MJS last updated on 06/Sep/18

$the man is 1 . 95 m tall, his beard is half as long$ $as Santa {Claus}^{'} . how many thorns has his$ $cactus if the temperature is 35 ° C ?$
Commented by tanmay.chaudhury50@gmail.com last updated on 06/Sep/18

$e x c e l l e n t . . . s i r . . . i h a v e t h o u g h t a v i r t u a l i m a g e$ $o f y o u s i r . . . i s h a l l p o s t . . . w h a t i i m a g i n e d a b o u t$ $y o u s i r . . .$
Commented by MJS last updated on 06/Sep/18

$ha! I^{'} d like to see it!$
Commented by math khazana by abdo last updated on 07/Sep/18

$w e a r e w a i t i n g t o k n o w s i r T i n k u t a r a, s i r A j f o u r, s i r M r w, s i r$ $R a u l, s i r P r a k a c h j a i n, s i r S m a i 3 . . .$
Commented by malwaan last updated on 07/Sep/18

Commented by malwaan last updated on 07/Sep/18

$that is me$
Commented by tanmay.chaudhury50@gmail.com last updated on 07/Sep/18

$t h a n k y o u s i r . . .$
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