Answer:
a) [tex]\frac{x^2}{4446^2}+\frac{y^2}{4420^2}=1[/tex]
b) Highest Altitude = 486 miles
Lowest Altitude = 460 miles
Step-by-step explanation:
a)
The standard form of equation of ellipse is:
[tex]\frac{x^2}{a^2}+\frac{y^2}{b^2}=1[/tex]
If a > b, then the major axis is horizontal.
If a < b, then the major axis is vertical.
Now, given:
a = 4446
b = 4420
We can write the equation of the ellipse as:
[tex]\frac{x^2}{a^2}+\frac{y^2}{b^2}=1\\\frac{x^2}{4446^2}+\frac{y^2}{4420^2}=1[/tex]
This is the equation, centered at origin.
b)
Since a > b, we can say that the major axis is horizontal and minor axis is vertical.
So, it stretches:
4446 miles from the center of the earth towards both -x and +x axis
and
4420 miles from the center of the earth towards both -y and +y axis
Since, the radius of the earth is 3960 miles, it means from center to earth's surface in all sides is 3960 miles.
The highest and lowest point altitude will be the different in x and y axis (horizontal and vertical) of the point with orbit of the satellite.
4446 - 3960 = 486 miles
and
4420 - 3960 = 460 miles
Thus,
Highest Altitude = 486 miles
Lowest Altitude = 460 miles
