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

Guest Jun 14, 2020

#1**0 **

Sorry, but the circle equation is not complete. It should be x^2 + y^2 = (missing part). What is that missing part?

MaxWong Jun 14, 2020

#5**0 **

First, you substitute y = (x - 3)/2 into x^2 + y^2 = 5.

You will get \(x^2 + \left(\dfrac{x - 3}2\right)^2 = 5\)

Now upon simplification, \(5x^2 - 6x - 11 = 0\).

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 \(\dfrac35\).

By a similar approach, you can find that the y-coordinate of the midpoint is \(-\dfrac65\), which means your answer is correct.

MaxWong Jun 14, 2020