Good morning,
For the question below, this is all the info that I get from the instructions. Can you please help me to complete the final steps? I'm really stuck.... Thank you very much.
Explanation (1)
Student Explanation
May 14, 2025
Hi AdorableApatosaurus7671! :)
Thank you for your question! :)
1) Knowing the area of the square is 5000, each of its sides equals √5000.
2) By Pythagoras' theorem, the diagonal (i.e., the diameter) is 100, so the radius is 50, which corresponds to "c" of the hyperbola.
3) If PA - PC = 60, then 2a = 60, so a = 30.
4) Using a² + b² = c², we find that b² = 1600.
5) The equation of the hyperbola is x²/900 - y²/1600 = 1, and the equation of the circle is x² + y² = 2500.
6) By substitution, we find y² = 1024, so x² = 1476, and x = 6√41.
7) The distance between the two x-values is therefore twice that, so d) 12√41.
I hope I answered your question! If you have any other questions, don’t hesitate to come back and see us!
Have a great evening! 😊
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