find the value of k such that k(x^2 +y^2 )+(y−2x+1)(y+2x+3)=0 is a circle hence obtain the centre and radius of the resulting circle.


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Question Number 57332 by problem solverd last updated on 02/Apr/19

$find the value of k such that$ $k (x^{2} + y^{2}) + (y - 2 x + 1) (y + 2 x + 3) = 0$ $is a circle hence obtain$ $the centre and radius of the$ $resulting circle .$
Commented by mr W last updated on 03/Apr/19

$k (x^{2} + y^{2}) + y^{2} - 4 x^{2} + . . . . = 0$ $(k - 4) x^{2} + (k + 1) y^{2} + . . . . = 0$ $f o r t h e e q u a t i o n o f a c i r c l e t h e$ $c o e f f i c i e n t s o f x^{2} a n d y^{2} m u s t b e t h e$ $s a m e .$ $k - 4 \overset{?}{=} k + 1 \Rightarrow n o s o l u t i o n f o r k$ $\Rightarrow t h e g i v e n e q u a t i o n c a n n o t b e a c i r c l e!$ $p l e a s e r e c h e c k t h e q u e s t i o n .$
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