WBJEE · Maths · Application of Derivatives
Let \(y=f(x)\) be any curve on the \(X-Y\) plane \& \(P\) be a point on the curve. Let \(C\) be a fixed point not on the curve. The length \(P C\) is either a maximum or a minimum, then
- A PC is perpendicular to the tangent at P
- B PC is parallel to the tangent at \(P\)
- C PC meets the tangent at an angle of \(45^{\circ}\)
- D PC meets the tangent at an angle of \(60^{\circ}\)
Answer & Solution
Correct Answer
(A) PC is perpendicular to the tangent at P
Step-by-step Solution
Detailed explanation
- Let \(P(x, y)\) be a point on the curve, and let \(C(a, b)\) be a fixed point not on the curve. - The distance \(d\) from \(C\) to \(P\) is given by \(d=\sqrt{(x-a)^2+(y-b)^2}\). - To find the extremum, we would set up an optimization problem for \(d\) with respect to the…
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