Question

A comet's path can be modeled by one branch of the hyperbola
y2
1096
􀀀
x2
41334
= 1;
where the sun is at the focus of that part of the hyperbola. Each unit of the coordinate
system is 1 milloion miles. nd the coordinates of the sun(assuming it is at the focus
with non-negative coordinates). Round to the nearest hundredth. How close does the
comet come to the sun?

Answer 1

Type it this way:
y^2 / 1096 - x^2 / 41334 = 1
or
x^2/41334 - y^2/1096 = -1

So you have a vertical hyperbola

Using your properties of a hyperbola x^2/a^2 - y^2/b^2 = -1
we know that c^2 = a^2 + b^2
c^2 = 41334 + 1096 = 42430
c = √42430 = appr 205.98
and the focal point is (0,205.98) , using only the positive value
since the positive vertex is (0,√1096) or appr(0,33.11)

the closest is ......
Don't forget your units are in millions.

Answer 2

Can i see the graph of this

Answer 3

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