Find The Point On The Curve y = x2 which Is Closest To The Point A(0, a).

Why Kaysons ?

Video lectures

Access over 500+ hours of video lectures 24*7, covering complete syllabus for JEE preparation.

Online Support

Practice over 30000+ questions starting from basic level to JEE advance level.

Live Doubt Clearing Session

Ask your doubts live everyday Join our live doubt clearing session conducted by our experts.

National Mock Tests

Give tests to analyze your progress and evaluate where you stand in terms of your JEE preparation.

Organized Learning

Proper planning to complete syllabus is the key to get a decent rank in JEE.

Test Series/Daily assignments

Give tests to analyze your progress and evaluate where you stand in terms of your JEE preparation.

SPEAK TO COUNSELLOR ? CLICK HERE

Download JEE Question paper & Solution Download JEE Important questions Download Complete syllabus of Maths, Physics, Chemistry

Question

Find the point on the curve y = x² which is closest to the point A(0, a).

None of these

diffcult

Solution

Correct option is

Using the parametric representation, consider an arbitrary point P (t, t²) on the curve.

Distance of P from A = PA

We have to find t so that this distance is minimum.

We will minimize PA²

Let PA² = f (t) = t² + (t² – a)²

We have to consider two possibilities.

Case I: a = 1/2

In this case, t = 0 is the only value.

Hence the closest point corresponds to t = 0

⇒ (0, 0) is the closest point.

Case II: a > ½

Hence the distance is minimum for

So the closest points are