In a solar system, two comets pass near the sun, which is located at the origin. comet e is modeled by quantity y plus 16 end quantity squared over 400 plus x squared over 144 equals 1 and comet h is modeled by quantity y plus 13 end quantity squared over 144 minus x squared over 25 equals 1 comma where all measurements are in astronomical units. part a: what are the vertices for the path of comet e

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meet024 meet024 · Answer 1 · 2022-06-29T15:15:00+02:00

The vertices of the path of the comet e are (-12,0) and (+12,0) as it is moving an elliptical path.

Given, that the Sun is located at the origin.

Comet e is modeled by

((y + 16)²)/400 + (x²)/144 = 1

This is an equation of an ellipse. So, the path traveled by Comet e is an elliptic path.

Comparing with the Standard equation of ellipse:

((y - k)²)/(b²)+ ((x - h) ²)/(a ²) = 1

whose, Centre is (h,k) and Vertex is (h±a, 0)

On Comparing Centre (h, k), h= 0 and k = -16 &

a²=144

a = 12

and,

b²=400

b=20

So, Centre (0, -16),

Vertex (-12,0) and (+12,0)

So, the vertices of the path of the comet e are (-12,0) and (+12,0).

Learn more about ellipse here:

https://brainly.com/question/16904744

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