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Hyperbola

Source: 2000 National High School Mathematics League, Exam One, Problem 3

March 10, 2020
conicshyperbolageometry

Problem Statement

A(−1,1)A(-1,1), B,CB,C are points on hyperbola x2−y2=1x^2-y^2=1. If △ABC\triangle ABC is a regular triangle, then the area of △ABC\triangle ABC is (A)33(B)332(C)33(D)63\text{(A)}\frac{\sqrt3}{3}\qquad\text{(B)}\frac{3\sqrt3}{2}\qquad\text{(C)}3\sqrt3\qquad\text{(D)}6\sqrt3\qquad
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