161 - Mathematics Questions Answers

blushblushConsider a branch of the hyperbola  x²-2y²-2√2x-4√2y-6=0, with vertex at the point A. Let B be one of the end points of its latus rectum .If C is the focus of the hyperbola nearest to the point A, then the area of the triangle ABC is ??????smiley

Asked By: AMIT DAS
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Joshi sir comment

 

x²-2y²-2√2x-4√2y-6=0 

Arrange this equation in form of standard hyperbola as 

(x-√2)2/4 - (y+√2)2/2 = 1

so X = x-√2, Y = y+√2

vertex coordinate :  X = 0 and Y = 0 so x = √2, y = -√2

similarly focus : X = ae, Y = 0,     here a = 2, b = √2 and b2 = a2(1-e2)

and end point of latus rectum : X = ae, Y = b2/a

solve the area and get the answer

 

 

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