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Question

If the normal to the rectangular hyperbola xy=c2 at the point (ct,ct) meets the curve again at (ct,ct),
then
 


A
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B
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C
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D
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Solution

The correct option is B
Equation of the tangent at (ct,ct) to the hyperbola xy=c2 is cxt+cty=2c2
Slope of the tangent =1t2 and slope of the normal =t2
Equation of the normal at (ct,ct) is yct=t2(xct)
If it passes through (ct,ct), then ctct=t2(ctct)(tt)=t3t(tt)t3t=1
 

Mathematics

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