+165 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.
+23252 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.
