IIT JEE , AIEEE Forum - Mathematics , Algebra

capricornabhi

Dear All,

I need your help. I am having the following problem and need a solution on an urgent basis.

SHOW THAT THE QUADRIC SURFACE x²+2xy-2xz= 1 IS A HYPERBOLIC CYLINDER.

Regards

Abhi

bvsatyaram

Very simple question,
The equation of a Hyperbolic Cylinder is (x2/a2)-(y2/b2)=1, where x2 denotes x^2.
here x=0 and y=0 are called principle axes
Refer to http://en.wikipedia.org/wiki/Quadric
The given equation can be written as,
( x+y-z )^2- (y-z)^2 = 1
Hence the given equation is a Hyperbolic Cylinder with x+y-z=0 and y-z=0 as principle axes.

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