the line x+y=2 cuts a circle x^2 +y^(2 ) =4 at two points. find the co−ordinates of points.


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Question Number 29365 by gyugfeet last updated on 08/Feb/18

$t h e l i n e x + y = 2 c u t s a c i r c l e x^{2} + y^{2} = 4 a t t w o p o i n t s . f i n d t h e c o - o r d i n a t e s o f p o i n t s .$
	Answered by Rasheed.Sindhi last updated on 08/Feb/18
	${ ((x+y=2)),((x^2 +y^(2 ) =4)) :}⇒ { ((y=2−x)),((x^2 +(2−x)^2 =4)) :} ⇒2x^2 −4x+4=4⇒x^2 −2x=0 ⇒x=0,2⇒y=2−0,2−2=2,0 (x,y)=(0,2) , (2,0) (0,2) and (2,0) are the coordinates of intersection points.$
	${\begin{cases} x + y = 2 \\ x^{2} + y^{2} = 4 \end{cases} \Rightarrow {\begin{cases} y = 2 - x \\ x^{2} + {(2 - x)}^{2} = 4 \end{cases}$ $\Rightarrow 2 x^{2} - 4 x + 4 = 4 \Rightarrow x^{2} - 2 x = 0$ $\Rightarrow x = 0, 2 \Rightarrow y = 2 - 0, 2 - 2 = 2, 0$ $(x, y) = (0, 2), (2, 0)$ $(0, 2) and (2, 0) are the coordinates of$ $intersection points .$
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