geometry of derivative: (a) Draw region enclosed by parab. y^2=4ax & latus rectum x=a
Having difficulty with the formulation of the equation from which the derivative is to be gained again.
Here is the question: "(a) Draw a diagram showing the region enclosed between the parabola y^2=4ax and its latus rectum x=a. (b) Find the dimensions of the rectangle of maximum area that can be inscribed in this region."
I can't draw here the graph but know it's a parabola on its side opening out on the RHS with the vertex at the origin being cut by the latus rectum from x=a
the latus rectum from point of contact to point of contact with the parabola is 4a long.
Pertinent is the area of the rectangle is Base x Height. But discerning these algebraically is difficult for me. One side of the rectangle lies along the latus rectum
and thus would be in terms of a and the other side would involve terms that come from the point of contact with the parabola but that is as far as I've got with my thinking. I have wondered if looking at it the other way round might be better. Thanks.
Having difficulty with the formulation of the equation from which the derivative is to be gained again.
Here is the question: "(a) Draw a diagram showing the region enclosed between the parabola y^2=4ax and its latus rectum x=a. (b) Find the dimensions of the rectangle of maximum area that can be inscribed in this region."
I can't draw here the graph but know it's a parabola on its side opening out on the RHS with the vertex at the origin being cut by the latus rectum from x=a
the latus rectum from point of contact to point of contact with the parabola is 4a long.
Pertinent is the area of the rectangle is Base x Height. But discerning these algebraically is difficult for me. One side of the rectangle lies along the latus rectum
and thus would be in terms of a and the other side would involve terms that come from the point of contact with the parabola but that is as far as I've got with my thinking. I have wondered if looking at it the other way round might be better. Thanks.