Question: If lines are drawn parallel to the coordinate axes through a point P on the parabola y 2 = kx, k > 0, the parabola

If lines are drawn parallel to the coordinate axes through a point P on the parabola y² = kx, k > 0, the parabola partitions the rectangular region bounded by these lines and the coordinate axes into two smaller regions, A and B.

a. If the two smaller regions are revolved about the y-axis, show that they generate solids whose volumes have the ratio 4:1.

b. What is the ratio of the volumes generated by revolving the regions about the x-axis? 0 A B y = kx P X

0 A B y = kx P X

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