Answer to Question #29122 in Analytic Geometry for alishan

Question

the line y--x=1 intersect the curve xy=6-2y at p and q calculate midpoint of pq

Answer 1

Let's find the intersection points of the line y-x=1 and the curve xy=6-2y. From the line equation we've got y=x+1 and substituting to
the curve equation we've got x(x+1)=6-2(x+1) or when simplify x^2+3x-4=0. There are two solutions of this equation: x1=1, x2=-4 hence as y=x+1, there are two intersection points: p=(1,2) and q=(-4,-3). The midpoint of pq is ((-4+1)/2, (-3+2)/2) = (-3/2, -1/2).