Question

an astronaut is to be fire into an elliptical orbit about the earth having a minimum altitude of 800km and a maximum altitude of 5400km find the equation of the curve followed by the astronaut consider the radius of the earth to be 6400km

Answer 1

Answer:

X^2/9100+y^2/6800=1

Step-by-step explanation:

using your numbers, we have

b = 6400+800 = 7200

a = 6400+5400 = 11800

So, just plug that into the standard equation for an ellipse, with center at (0,0)

Answer 2

The equation of the ellipse is $\rm \dfrac{x^{2} }{7200} } + \dfrac{y^{2} }{11800} } = 1$.

Ellipse

Ellipse is a locus of a point that moves in a plane such that the sum of its distances from the two points is called foci. It is taken from the cone by slicing it at an angle.

Given

The earth has a minimum altitude of 800km and

A maximum altitude of 5400km.

Astronauts consider the radius of the earth to be 6400km.

To find

The equation of the curve is followed by the astronaut.

How to find the equation of the curve followed by the astronaut?

The earth has a minimum altitude of 800km and

A maximum altitude of 5400km.

Astronauts consider the radius of the earth to be 6400km.

The equation of the ellipse is given by

$\rm \dfrac{x^{2} }{a^{2} } + \dfrac{y^{2} }{b^{2} } = 1$

Then

a² = 6400 + 800 = 7200

b² = 6400 + 5400 = 11800

Then the equation of ellipse will be

$\rm \dfrac{x^{2} }{7200} } + \dfrac{y^{2} }{11800} } = 1$

Thus, the equation of the ellipse is $\rm \dfrac{x^{2} }{7200} } + \dfrac{y^{2} }{11800} } = 1$.

More about the ellipse link is given below.

https://brainly.com/question/19507943