{"id":237171,"date":"2025-06-17T04:26:02","date_gmt":"2025-06-17T04:26:02","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=237171"},"modified":"2025-06-17T04:26:04","modified_gmt":"2025-06-17T04:26:04","slug":"if-the-light-from-a-lamp-casts-a-hyperbolic-shadow-pattern-on-the-wall-calculate-the-equation-of-the-hyperbola-if-the-distance-between-the-vertices-is-2-feet-and-the-foci-are-half-a-foot-from-the-ver","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/06\/17\/if-the-light-from-a-lamp-casts-a-hyperbolic-shadow-pattern-on-the-wall-calculate-the-equation-of-the-hyperbola-if-the-distance-between-the-vertices-is-2-feet-and-the-foci-are-half-a-foot-from-the-ver\/","title":{"rendered":"If the light from a lamp casts a hyperbolic shadow pattern on the wall, calculate the equation of the hyperbola if the distance between the vertices is 2 feet and the foci are half a foot from the vertices."},"content":{"rendered":"\n

If the light from a lamp casts a hyperbolic shadow pattern on the wall, calculate the equation of the hyperbola if the distance between the vertices is 2 feet and the foci are half a foot from the vertices.<\/p>\n\n\n\n

The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n

Correct Answer:<\/strong><\/p>\n\n\n\n

The equation of the hyperbola is:x212\u2212y2(0.5)2=1\\frac{x^2}{1^2} – \\frac{y^2}{(0.5)^2} = 112×2\u200b\u2212(0.5)2y2\u200b=1<\/p>\n\n\n\n

or simplified:x21\u2212y20.25=1\\frac{x^2}{1} – \\frac{y^2}{0.25} = 11×2\u200b\u22120.25y2\u200b=1<\/p>\n\n\n\n

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Explanation:<\/strong><\/p>\n\n\n\n

A hyperbola is a set of all points such that the difference<\/strong> of the distances to two fixed points (called foci<\/em>) is constant. The standard form of a horizontal<\/strong> hyperbola centered at the origin is:x2a2\u2212y2b2=1\\frac{x^2}{a^2} – \\frac{y^2}{b^2} = 1a2x2\u200b\u2212b2y2\u200b=1<\/p>\n\n\n\n

In this equation:<\/p>\n\n\n\n