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Conics Problem

Source: 2005 National High School Mathematics League, Exam One, Problem 5

March 19, 2020
conicsellipsehyperbola

Problem Statement

Which kind of curve does the equation x2sin⁡2−sin⁡3+y2cos⁡2−cos⁡3=1\frac{x^2}{\sin\sqrt2-\sin\sqrt3}+\frac{y^2}{\cos\sqrt2-\cos\sqrt3}=1 refer to? (A)\text{(A)} An ellipse, whose focal points are on xx-axis. (B)\text{(B)} A hyperbola, whose focal points are on xx-axis. (C)\text{(C)} An ellipse, whose focal points are on yy-axis. (D)\text{(D)} A hyperbola, whose focal points are on yy-axis.
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