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Question

If t is a parameter then x=at+1t and y=bt-1t represents


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Solution

Explanation for the correct option:

Finding the relation between x and y:

We need to eliminate t to find the relation between x and y,

Given equation x=at+1t and y=bt-1t can be rewritten as

xa=t+1t...i

yb=t-1t...ii

squaring equation i, we get

xa2=t+1t2x2a2=t2+1t2+2...iii

squaring equation ii, we get

yb2=t-1t2y2b2=t2+1t2-2...iv

Substracting equation iv from iii

x2a2-y2b2=t2+1t2+2-t2-1t2+2

x2a2-y2b2=4x22a2-y22b2=1

which is the general equation of hyperbola x2a2-y2b2=1

Hence, the relation between x and y represents the general equation of hyperbola.


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