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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

{\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 .