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Question

xy=a2 and x2+y2=2a2
These two curves :

A
touch.
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B
intersect
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C
never intersect
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D
none of the above
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Solution

The correct option is A touch.
Touch: The two curves meet where (x2a2)=0
x=a,a and so y=a2x=a or a.
Hence the points are (a,a) or (a,a).
dydx1=yx=1.dydxII=xy=1
Hence the curves touch.

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