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Question

Let normal at point P(1,2) on the curve xy=2 meets the curve again at point Q, then the value of 4PQ25=

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Solution

Let the point Q(t,2t)
For slope of tangent , y=2x
dydx=2x2
(dydx)(1,2)=2
slope of normal =1slope of tangent
slope of normal =12=slope of PQ
12=2t2t1
t2+3t4=0
(t+4)(t1)=0
t=4,1
Q(4,12),p(1,2)
PQ2=1254
4PQ25=25

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