Thank you for visiting An architect designs two houses that are shaped and positioned like a part of the branches of the hyperbola whose equation is tex 1225y 2. This page is designed to guide you through key points and clear explanations related to the topic at hand. We aim to make your learning experience smooth, insightful, and informative. Dive in and discover the answers you're looking for!
Answer :
The closest distance between the houses designed by the architect is 70 yards.
The equation of the hyperbola is transformed into its standard form to determine that the closest distance between the houses is at the vertices along the transverse axis, which is calculated to be 70 yards apart.
The equation of the hyperbola given is 1225y2 - 625x2 = 765,625, which can be rewritten in the standard form of a hyperbola by dividing through by 765,625. This yields the equation (y2)/(c2) - (x2)/(a2) = 1, where a2 = 765,625/625 and c2 = 765,625/1225.
Simplifying, we find a2 = 1225 and c2 = 625. This gives us the values a = 35 and c = 25. The closest distance between the branches of the hyperbola is 2a, since the closest points occur at the vertices of the hyperbola on the y-axis (the transverse axis for a vertical hyperbola).
Therefore, to find the closest distance between the houses designed by the architect, we calculate 2a, which equals 2*35 = 70 yards.
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