Secondary V • 2mo.
Hi, I just wanted to know if these steps and calculations are good for this question or if I am missing important steps. Thank you.
Hi, I just wanted to know if these steps and calculations are good for this question or if I am missing important steps. Thank you.
Explanation from Alloprof
This Explanation was submitted by a member of the Alloprof team.
Hi HonourableDragon6239,
Thank you for your question :)
It’s a bit hard to answer precisely, since I’m not entirely sure what your reference system was when you did the problem. Nevertheless, here’s an explanation of the steps, see if they match your solution :)
The simplest way to start is to place the vertex of the smaller parabola at the origin. This means the conic equation is x^2=4cy. We use the conic equation because both parabolas share the same focus. Given that the longest cable is 10 m and the bridge is made of 16 segments of 2 m each, we can say that one coordinate of the small parabola is (-16, -10), since the bridge is symmetrical. With this information, you can find the value of c in the equation and plot it on your graph.
Since the focus is located at the same coordinates for both parabolas, we can deduce that the c value for the second parabola is 1 m more, as its vertex is 1 m higher than that of the first parabola and that c is the distance between vertex and focus. Also, using the vertex coordinates of the second parabola (0, 1), you can determine its equation. If you need examples, you can check out this page: https://www.alloprof.qc.ca/en/students/vl/mathematics/parabola-conic-m1330
Finally, since we know the bridge is 6 m above the highway, we can say the base of the pillars has a y-coordinate of -16. The last step is to calculate the full coordinates of each parabola for y=−16, so you can measure the distances.
Don’t hesitate to ask if you have more questions! 😊
Sandrine