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  • The locus of a point which moves so that the sum of its distances from two fixed points <img alt="\ma

The locus of a point \mathrm{P} which moves so that the sum of its distances from two fixed points \mathrm{A(2,0)\: and \: B(-2,0)} is equal to 6 units is a


 

Option: 1

circle
 


Option: 2

parabola
 


Option: 3

ellipse
 


Option: 4

hyperbola
 


Answers (1)

best_answer

\mathrm{\quad P A+P B=6} Let \mathrm{P \: \: be \: \: (h, k).}

\mathrm{ \Rightarrow \sqrt{(h+2)^2+k^2}+\sqrt{(h-2)^2+k^2}=6 }

As R.H.S is greater than distance \mathrm{A B }, the locus of \mathrm{P(h, k) } is an ellipse with foci at \mathrm{A \: and\: B. }

Hence option 3 is correct.

Posted by

Nehul

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