Question

the line y=mx+c intersect at y=x^2 in points A,B.Find the point P on the arc AOB of the parabola that maximises the area of the triangle PAB

Answer 1

equate 2 lines
x^2=mx+c
x2-mx+c=0
point A
x=m+root(m2-4mc)/2 y=square(m+root(m2-4mc)/2)
point b
x=m+root(m2-4mc)/2 y=square(m-root(m2-4mc)/2)

Answer 2

\[x=(m \pm \sqrt{4b+m^2})/2\]

Answer 3

these co-ordinate seems to be the co-ordinates of A,B,not for P

Answer 4

How do we maximise area