Question
Mathematics Question on Fundamental Theorem of Calculus
Let P and Q be any points on the curves (x – 1)2 + (y + 1)2 = 1 and y = x2, respectively. The distance between P and Q is minimum for some value of the abscissa of P in the interval
A
(0,41)
B
(21,43)
C
(41,21)
D
(43,1)
Answer
(41,21)
Explanation
Solution
The correct answer is (C) : (41,21)
y=mx+2a+m21 ( Equation of normal to x2 = 4ay in slope form)through(1,-1)
4m3+6m2+1=0
⇒m≃−16
Slope of normal ≃5−8=tanθ
⇒cosθ≃89−5,sinθ≃898
xp=1+cosθ≃1−895∈(41,21)