an ellipse has a center at the origin , a vertex along the major axis at (13,0), and a focus at (12,0). What is the equation of
1 answer:
Answer:
The answer to your question is below
Step-by-step explanation:
Data
Center = (0, 0)
Vertex = (13, 0)
Focus = (12, 0)
Process
From the data we know that it is a horizontal ellipse.
1.- Calculate "a", the distance from the center to the vertex.
a = 13
2.- Calculate "c", the distance from the center to the focus
c = 12
3.- Calculate b
Use the Pythagorean theorem to find it
a² = b² + c²
-Solve for b
b² = a² - c²
-Substitution
b² = 13² - 12²
-Simplification
b² = 169 - 144
b² = 25
b = 5
4.- Find the equation of the ellipse
or
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Answer:
ascend
Step-by-step explanation:
There are a couple of ways to figure this. One is to look at the partial derivative ...
The sign of it is negative, so when y decreases, z increases. Going south means decreasing the y-coordinate, so moving in that direction will cause you to ascend.
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Another way to figure this is to evaluate z for some small movement in the southerly direction. In the attached, we find that moving 1 m south to (120, 79, 1165.59) causes an elevation increase of about 1.6 m. Walking south causes you to ascend.
Note that this is consistent with our first result, as -0.02y = -0.02(80) = -1.6. So a change in y of -1 should cause a change in z of about (-1.6)(-1) = 1.6.
