Find the values for a, b, and c that complete the simplification.
1 answer:
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We have the following equation:
If we graph this equation we realize that in fact this is an ellipse with major axis matching the y-axis. So we can recognize these characteristics:
1. Center of the ellipse:
The midpoint C<span> of the line segment joining the foci is called the </span>center<span> of the ellipse. So in this exercise this point is as follows:
</span>
2. Length of major axis:
The line through the foci is called the major axis<span>, so in the figure if you go from -5, at the y-coordinate, and walk through this major axis to the coordinate 1, the distance you run is the length of the major axis, that is:</span>
3. Length of minor axis:
The line perpendicular to the foci through the center is called the minor axis. So in the figure if you go from -2, at the x-coordinate, and walk through this minor axis to the coordinate 2, the distance you run is the length of the minor axis, that is:
4. Foci:
Let's find c as follows:
Then the foci are:
If we graph this equation we realize that in fact this is an ellipse with major axis matching the y-axis. So we can recognize these characteristics:
1. Center of the ellipse:
The midpoint C<span> of the line segment joining the foci is called the </span>center<span> of the ellipse. So in this exercise this point is as follows:
</span>
2. Length of major axis:
The line through the foci is called the major axis<span>, so in the figure if you go from -5, at the y-coordinate, and walk through this major axis to the coordinate 1, the distance you run is the length of the major axis, that is:</span>
3. Length of minor axis:
The line perpendicular to the foci through the center is called the minor axis. So in the figure if you go from -2, at the x-coordinate, and walk through this minor axis to the coordinate 2, the distance you run is the length of the minor axis, that is:
4. Foci:
Let's find c as follows:
Then the foci are:
Answer:
See below
Step-by-step explanation:
<em>Refer to attached. All answers included.</em>
- <u>Note. Will mainly refer to y-coordinates in distance questions</u>
- Distance from coffee shop to library: 16 -8 = 8
- Distance from coffee shop to school: 16 - 10 = 6 = x
- Distance from school to library: 10 - 8 = 2 = y
- Ratio x:y = 6: 2 = 3:1
- Distance from Sergio's home to Saskia's home: 19 -3 = 16
- Distance from Sergio's home to Post office: 16*1/4 = 4
- Coordinates of post office: x = 16+4/4= 17, y = 19-16/4= 15
- Distance from Kay's home to twin theater: 20 - 4 = 16
- Distance from twin theater to market: 16*3/4 = 12
- Coordinates of market: x = 5+4/4= 6, y = 4 + 16/4= 8
