Aryan coordinate challenge 4

Geometry Level 4

Let the equation of a hyperbola be 2 x 2 + 2 y 2 + 4 x + 5 y + 5 x y + 4 = 0 2x^2+2y^2 + 4x + 5y + 5xy + 4= 0 . If ( 81 , a ) (81,a) is lying on tranverse axis, find the value of a a .


The answer is -82.

Aryan Goyat by aryan goyat , 22, India

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2 solutions

Mark Hennings
Jul 11, 2016

The curve has equation 9 ( x + 1 + y ) 2 − ( x + 1 − y ) 2 + 8 = 0 9(x+1+y)^2 - (x+1-y)^2 +8 = 0 the transverse axis, which passes through both foci, has equation y = − x − 1 y = -x-1 That is the axis which meets the hyperbola in two places - at x = − 1 ± 2 x = -1 \pm \sqrt{2} . The correct answer to this question should be − 82 \boxed{-82} . @Calvin Lin

0 Helpful 0 Interesting 0 Brilliant 0 Confused

Thanks. I have updated the answer to -82.

Calvin Lin Staff - 4 years, 11 months ago
Aryan Goyat
Dec 4, 2015

0 Helpful 0 Interesting 0 Brilliant 0 Confused

Please check your work. I obtain y = − x − 1 y = -x - 1 as the equation instead.

Calvin Lin Staff - 4 years, 11 months ago

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