Find the eccentricity of the conic given by: (xtan⁡10∘+ytan⁡20∘+tan⁡30∘)(xtan⁡120∘+ytan⁡220∘+tan⁡320∘)+2018=0

Sereinserenormg

Sereinserenormg

Answered

2022-01-26

Find the eccentricity of the conic given by:
(xtan10+ytan20+tan30)(xtan120+ytan220+tan320)+2018=0

Answer & Explanation

ataill0k

ataill0k

Expert

2022-01-27Added 18 answers

Equating to 0 the expressions inside the parentheses we get the equations of two lines, which are the asymptotes of the hyperbola:
xtan10+ytan20+tan30=0,   xtan60+ytan40+tan320=0,
where I used tan120=tan60 and tan220=tan40
But these lines are perpendicular, because
tan10tan60=tan20tan40
(remembering that tan60=1tan30).
Hence this is a rectangular hyperbola and its eccentricity is 2.

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