The paraboloid intersects the plane in a parabola. Find parametric equations for the tangent line to this parabola at the point . Use a computer to graph the paraboloid, the parabola, and the tangent line on the same screen.
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Tangent Lines and Normal Lines
(a) Find an equation of the tangent line to the parabola at the point (2,4).
(b) Find an equation of the normal line to at the point (2,4). (The normal line at a point is perpendicular to the tangent line at the point.) Where does this line intersect the parabola a second time?
(c) Find equations of the tangent line and normal line to at the point (0,0).
(d) Prove that for any point (a, b)
(0,0) on the parabola , the normal line intersects the graph a second time.
(a) Find an equation of the tangent line to the parabola y =x2 at the point (2,4)
(b) Find an equation of the normal line to y=x2 at the point (2,4).
(The normal line at a point is perpendicular to the tangent line at the point). Where does this line intersect the parabola a second time?
(c) Find equations of the tangent line and normal line to y=x2 at the point (0,0).
(d) Prove that for any point (0,0) on the parabola y=x2, the normal line intersects the graph a second time.
(a) The plane intersects the cylinder in an ellipse. Find parametric equations for the tangent line to this ellipse at the point .
(b) Graph the cylinder, the plane, and the tangent line on the same screen.
