document.write( "Question 1158584: Draw the line y = 2x−5 and the circle x2 +y2 = 5. Use algebra to show that these graphs touch at only one point. Find the slope of the segment that joins this point to the center of the circle, and compare your answer with the slope of the line y = 2x − 5. \n" ); document.write( "

Algebra.Com's Answer #781552 by Shin123(626) $\"\"$ $\"About$

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Using Desmos to make a graph, we get

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$\"system%28y=2x-5%2Cx%5E2%2By%5E2=5%29\"$ . Substituting 2x-5 for y in the second equation, we get $\"x%5E2%2B%282x-5%29%5E2=5\"$ . Expanding, we get $\"5x%5E2-20x%2B25=5\"$ . Dividing both sides by 5 we get $\"x%5E2-4x%2B5=1\"$ . $\"%28x-2%29%5E2=0\"$ . So x=2 and plugging in to the first equation, we get y=-1. So the two graphs intersect at only one point and that point is (2,-1). The slope of the segment between (0,0) and (2,-1) is $\"-1%2F2\"$ . $\"-1%2F2%2A2=-1\"$ . This means that the segment and the line are perpendicular. The graph with the segment is

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