1.

Asymptotes of the curve x^2y^2=a^2(x^2+y^2) form a square of side 2a

Answer»

Axx2+bxy2=1axx2+bxy2=1

Rearranging this into a nicer form:

y2=−b2∗x2a2−x2y2=−b2∗x2a2−x2

A VERTICAL ASYMPTOTE will OCCUR when the denominator = 0.Therefore :

x=+/−ax=+/−a

For the HORIZONTAL asymptope take the limit as x → infinity

y2=limx→infinity−b2∗x2x2a2x2−1y2=limx→infinity−b2∗x2x2a2x2−1

y2=limx→infinityb21y2=limx→infinityb21

Therefore Horizontal assomtyopes at :

y=+/−b


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