Thread: 2 more conics questions.

1)find an equation of the hyperbola with center (2,3), a focus at (2,5), and a focal chord of length 6.


2)a section of roller coaster track is shaped of a parabola. The track spans a horizontal distance of 84 yards and has a maximum height of 32 yards. Six vertical support beams are located at a distance of 12 yards from each other. Find the sum of the lengths of all six vertical beams.

#2:

Find the equation of your parabola. The vertex is at (0,32)

and it passes through (42,0)

y=a(x-h)^2+k

0=a(42-0)^2+32

a=-8/441

The parabola equation is y=-8x^2/441+32

Can you continue from there?. We centered the parabola at the origin.

Space your beams accordingly. You could put the first one to the right at x=6, then x=18, then x=30.

The same to the left. Add up all your y values.