JEE Main 2015MathematicsCircleHardMCQ

JEE Main 2015 — Circle Question with Solution

JEE Main 2015 (10 Apr Online)

Question

Let the tangents drawn to the circle, x2+y2=16 from the point P0,h meet the x-axis at points A and B. If the area of ΔAPB is minimum, then positive value of h is:

Choose an option

Show full solutionCorrect option: A
Correct answer
A42

Step-by-step explanation



Let equation of tangent be xcos⁡ α+ysin⁡ α=4

Now, its points of intersection with co-ordinate axis are 

A4cosα,0, P0,4sinα

Now, ar∆PAB=2ar∆PAO

=2×12OA×OP

=4sin⁡α  . 4cos⁡α=32sin⁡2α≥32

which is maximum if, α=π4 

∴   P0,4sin⁡π4

∴   h=42

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About this question

This is a previous-year question from JEE Main 2015, covering the Circle chapter of Mathematics. PrepSharp catalogues every PYQ from JEE Main with a verified answer key and step-by-step solution prepared by IIT alumni — so you can search by chapter, topic or year and revise efficiently.