Imagine a plane and a cone intersecting to form a parabola b)Imagine the plane moving so that it keeps the same angle, but its point of intersection with the axis moves in the direction of the apex of the cone and eventually passes through the apex. Describe with happens to the parabola and write equations that describe how the parabola changes.

Question

therealone21-1 · Answer

When the plane passes through the apex, the intersection of the (double) cone and the plane will be a line on the double-cone that passes through the apex of the cone. As the plane moves toward the apex, the parabola appears more "pointy".

therealone21-1 · Answer

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shaeelynn · Answer

can you help me write the equations that describe the parabola change

dumbcow · Answer

as the plane gets closer to the apex, the parabola appears to get steeper

$$y = a x^2$$
when "a" is larger the steeper the parabola
so when plane is approaching apex, the value of "a" is increasing

shaeelynn · Answer

i still dont get it

amilapsn · Answer

First  you can write an equation of a double cone. Then equation of a plane intersecting with the cone to form a parabola. Can you do it?