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Hyperbola

Hyperbola

by Vibhavari Dasagi -
Number of replies: 2

The asymptotes of a hyperbola given by x = a tan(q + a),  and y =  b tan(q + b)  where q is variable parameter is______( c is any constant)

a) cxy - bx + ay + abc = 0

b) bcx + aby + acxy + abc = 0

c) xy + y2 + a + b + c = 0

d) (a + b)x + (c +a)y + (b + c)xy = 0

Please give me the solution to the above problem. 

In reply to Vibhavari Dasagi

Re: Hyperbola

by Manish Verma -
Removing the parameter q and converting the equation in cartesian form we get,
ay - bx + xytan(a-b) + abtan(a-b)=0.

Now, asymptotes differ from the equation of hyperbola only by a constant, the terms involving variables remaining the same irrespective of the form of the hyperbola.

Hence, the equation of the asypototes should be of the form,
ay - by + xytan(a-b) + constant = 0.

Out of the options given only one option satisfies this condition.

However, someone interested in going further can use the condition of pair of lines (abc + 2fhg - af2 - bg2 - ch2 = 0) to find the constant.