The line y+x=9 intersects the curve y=x^2-2x+3 at the points P and Q .

Question

(a) Find the coordinates of P and Q .
(b) Sketch the line and the curve on the same set of axes.
(c) Calculate the area enclosed by the line and the curve.

Answer 1

Set the two equations equal to each other and solve
Go look at your integration chapter - area bounded by two curve
Integration (line - parabola)dx
Then you are going to deal with adding the part of the parabola under the x-axis