Hello I need help on this problem. I need someone to explain, solve, and anserr this question. I am a visual learner and I need someone solve and the answer. Thank you.

Question

The guardians of the galaxy have to travel in the spaceship Milano from Xander, located on the star map at (-4,-8) to Titan, located at (6,12), to help the avenger stop Thanos. Unfortunately, the fastest route, y=2x, will fly them through an elliptical asteroid field, represented by the equation x^2/16+y^2/4=1. They will travel an average of 0.57 miles per hour, but they must slow down to navigate the asteroid field. While in the field, they will average 0.38 miles per hour. How long will it take them to make the trip?

Answer 1

Since you are a visual learner, draw and label a diagram!

That includes both the ellipse and the line joining (-4, -8) and (6, 12).

Determine the equation of the line between (-4, -8) and (6, 12).

Use the two-point form from Algebra 1.

Determine the points of intersection (two!) between the line and the ellipse.

Determine the distance from (-4. -8) and the left point of intersection

Determine the distance between (-4, -8) ad (6, 12).

Determine the distance between the right point of intersection and (6, 12).

Use the three distances with the related rates to determine the travel time in each of the three segments.

Add the three times for the total time of the trip.