Braxton Pugh

2021-08-19

To find: The points where the comet might intersect the orbiting planet.

It is given that the planet's orbit follows a path described by$16{x}^{2}+4{y}^{2}=64$ .

Given that a comet follows the parabolic path$y={x}^{2}-4$ .

It is given that the planet's orbit follows a path described by

Given that a comet follows the parabolic path

Cullen

Skilled2021-08-20Added 89 answers

Procedure used:

An Application of a Nonlinear System:

Step 1: Write a system of equations modeling the conditions in the problem.

Step 2: Solve the system and answer the question asked in the problem.

Step 3: Check the proposed solution in the original wording of the problem."

Calculation:

Multiply

Add the both equations and obtain the result as follows.

On further simplification gives,

Substitute

Substitute

Thus, for

Thus, the solution set is

Check the result, by substituting the obtained solutions in the given original equations

Substitute (2.0) in the given system and check.

Substitute (-2,0) in the given system and check.

Substitute (0,-4) in the given system and check.

Therefore, the points where the comet might intersect the orbiting planet are

$\frac{20b}{{\left(4{b}^{3}\right)}^{3}}$

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