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The line y=(x-3)/2 intersects the circle x^2+y^2=5 at C and D. Find the coordinates of the midpoint of CD.

 Aug 4, 2020
 #1
avatar+21953 
+1

y  =  (x - 3) / 2                                 x2 + y2  =  5

 

Step 1)  Substitute  (x - 3)/2  for y into the equation  x2 + y2  =  5

              --->     x2 + [ (x - 3)/2 ]2  =  5

              Square: 

              --->     x2 + (x2 - 6x + 9) / 4  =  5

              Multiply each term by 4:

              --->    4x2 + (x2 - 6x + 9)  =  20

              Simplify:

               --->    5x2 - 6x - 11  =  0

 

Step 2)  Use the quadratic formula to find the two solutions:  x1  and  x2.

 

Step 3)  Replace  x1  into the equation y  =  (x - 3) / 2  to find the value of  y1.

              You now have the point  ( x1, y1 ).

              

              Replace  x2  into the equation y  =  (x - 3) / 2  to find the value of  y2.

              You now have the point  ( x2, y2 ).

 

Step 4)  Use the midpoint formula to find your answer.

 Aug 4, 2020
 #2
avatar+71 
+2

Thank you! :)

viola  Aug 4, 2020

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