Week 3: Designer Tables (Conics)

1. The Two Pillars (Circles) 📍 Answer Key: Pillars

"Two pillars... sitting inside the table."
Model the Outer and Inner circles for both Left and Right pillars.

Distance ($c$):

Outer ($R$): Inner ($r$):

Correct Solution

1. Offset: Answer key puts pillars at $x = \pm 100$. So $c=100$.

2. Outer Radius: Diameter 70cm $\rightarrow R = 35$.

3. Inner Radius: Base diameter 50cm $\rightarrow r = 25$.

Equations: $(x \pm 100)^2 + y^2 = 35^2$ and $25^2$.

2. The Tabletop 📍 Page 1: Diagram 2

Select a model to enclose the pillars.

Vertices at $\pm 180$. Passes through $(0, 60)$.

$y^2 = $ $(x \pm 180)$

Correct Solution (Parabola)

1. Form: $y^2 = k(x+180)$ (Left side).

2. Point: At center $x=0$, width is 120, so $y=60$.

3. Sub: $60^2 = k(0+180) \Rightarrow 3600 = 180k$.

4. Solve: $k = 20$.

Eq: $y^2 = 20(x+180)$ and $y^2 = -20(x-180)$.