What are the points of contact that the line of 2x plus y equals 5 makes with the curve of x squared -y squared equals 3 showing work?

Answer 1

If: 2x+y = 5 then y = 5-x

If: x^2 - y^2 = 3 then x^2 -(5-x)^2 = 3

So: x^2 -(25 -20x +4x^2) = 3

Removing the brackets and subtracting 3 from both sides: -3x^2-28+20x = 0

Using the quadratic equation formula: x = 14/3 or x = 2

Therefore by substitution points of contact are at: (14/3, -13/3) and (2, 1)