Question

Will you please check my work for me.
1)The equation of a parabola is shown.
y=1/14X^2. What are the coordinates of the focus?
(0,-3.5) <----
(0,-4)
(0,7)

2)The equation x2 + (y + 3)2 = 36 models the boundary on a local map for which Darren can hear his friend Tom on his two-way radio when Darren is at home. How far (in miles) can Tom walk from Darren's home and still be heard?
3 miles

6 miles<----

2 miles

12 miles

3)A plane intersects only one nappe of a double-napped cone. It is neither perpendicular to the cone's axis nor parallel to its generating line. Which conic section is formed?

point

circle

ellipse <-----

parabola

Answer 1

1. Y = (1/14)x^2.

V(h,k)
h = Xv = -b/2a = 0 / (1/7) = o.
k = Yv = (1/14)*0^2 = 0.

4a = 4(1/14) = 4/14 = 2/7.
1/4a = 7/2.

V(0,0), F(0,y).
VF = y-0 = 1/4a = 7/2
y-0 = 7/2
Y = 7/2 = 3.5.

F(0,3.5).