The line y = (x-3)/2 intersects the circle x^2 + y^2 at A and B. Find the coordinates of the midpoint of AB.
This is real urgent thank you
Sorry, but the circle equation is not complete. It should be x^2 + y^2 = (missing part). What is that missing part?
First, you substitute y = (x - 3)/2 into x^2 + y^2 = 5.
You will get x2+(x−32)2=5
Now upon simplification, 5x2−6x−11=0.
Notice that the solutions to this equation is the x-coordinates of A and x-coordinates of B respectively.
We conclude that the x-coordinate of the midpoint of AB is the sum of roots divided by 2, which is 35.
By a similar approach, you can find that the y-coordinate of the midpoint is −65, which means your answer is correct.