a) The points A (–2, 1) and B (4, 4) lie on the
parabola y = x2
/4. Let l be the line parallel
to AB and tangent to the parabola. If
C is the point of tangency, then the area
of triangleABC gives a rough approximation of
the area bounded by AB and the parabola.
Find the coordinates of C and also the area
of triangleABC

Question

a) The points A (–2, 1) and B (4, 4) lie on the
parabola y = x2
/4. Let l be the line parallel
to AB and tangent to the parabola. If
C is the point of tangency, then the area
of triangleABC gives a rough approximation of
the area bounded by AB and the parabola.
Find the coordinates of C and also the area
of triangleABC

anonymous · Answer

b)  let
j and k be lines tangent to the parabola and
parallel to AC and BC, respectively. Let D
and E be the respective points of tangency.
Find the coordinates of D and E and the
areas of tirangleADC and triangleBEC. Add the areas
of the three triangles to improve the area
approximation found for part a