I I need help on checking if this is right. Is someone abke to show me the answer for this wuestion for my review. I know waht to do i just need clarification.

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 0.53 miles per hour, but they must slow down to navigate the asteroid field. While in the field, they will average 0.39 miles per hour. How long will it take them to make the trip?

Answer 1

Draw and label a diagram - the line joining (-4, -8) and (6,12) as well as the ellipse.

Three distances must be determined, from (-4. -8) to intersection of line and left side of ellipse, from one side of the ellipse to the other, and from the right side of the ellipse to (6, 12)

Determine the equation of the line from (-4. -8) to (6, 12)

Determine the two point of intersection of the line and the ellipse.

Determine the distance from (-4, -8) to left point of intersection;

Determine the distance between the two points of intersection (across ellipse).

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

Use the distance formula (d = r t) to determine time of each segment.