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Hi HonourableDragon6239,

Thank you for your question! :)

The challenge with this exercise is that we need to find the right coordinates to help us determine the equations of the functions in this situation.

To begin, you’ll need to find the equation of the parabola. Based on the diagram and the symmetry, we can deduce that the zeros are located 120 cm from the center, and the vertex has coordinates (0, -60). With that information, you’ll be able to write the equation of the parabola, which will be useful later on :)

Next, we need to find the equation of the hyperbola. This part is a bit trickier, since we don’t know the coordinates of the vertex. However, from the diagram, we can see that the hyperbola passes through the point (-40, -120). Also, based on the information in the problem, we can deduce that the distance from the center to each focus is 100 cm. You can then use the Pythagorean theorem to have a first equation as shown in this image:

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With c=100, you can have c^2=a^2 +b^2 as your first equation, and x^2/a^2 - y^2/b^2 = 1 as your second equation by substituting the point (-40, -120) for x and y. That system will allow you to find the values of a and b. Here is a link that could help you to find the equation: https://www.alloprof.qc.ca/en/students/vl/mathematics/hyperbola-conic-m1329

Once you have the equation of the hyperbola, the last step is to find the points of intersection between the geometric figures (the parabola and the rectangle), in order to determine the coordinates of points A, B, C, and D :)

Don’t hesitate to reach out if you have more questions!

Sandrine