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Problem If x a cos α + y b sin α = 1 \frac{x}{a} \cos \alpha + \frac{y}{b} \sin \alpha = 1 a x cos α + b y sin α = 1 x a cos β + y b sin β = 1 \frac{x}{a} \cos \beta + \frac{y}{b} \sin \beta = 1 a x cos β + b y sin β = 1 cos α cos β a 2 + sin α sin β b 2 = 0 \frac{\cos \alpha \cos \beta}{a^2} + \frac{\sin \alpha \sin \beta}{b^2} = 0 a 2 c o s α c o s β + b 2 s i n α s i n β = 0 tan α tan β = b 2 ( x 2 + a 2 ) a 2 ( y 2 + b 2 ) \tan \alpha \tan \beta = \frac{b^2(x^2 + a^2)}{a^2(y^2 + b^2)} tan α tan β = a 2 ( y 2 + b 2 ) b 2 ( x 2 + a 2 ) x 2 + y 2 = a 2 + b 2 x^2 + y^2 = a^2 + b^2 x 2 + y 2 = a 2 + b 2 tan α tan β = a 2 b 2 \tan \alpha \tan \beta = \frac{a^2}{b^2} tan α tan β = b 2 a 2 Browse the problem library