Question

║⊕QUESTION⊕║
If a man's wit is wandering, let him study mathematics.
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CLASS 11
THE CARTESIAN COORDINATE SYSTEM
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Find the locus of a point P which moves so that the sum of the squares of its distance from A(3,0) and B(-3,0) is four times the distance between A and B.

Answer 1

Answer:

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Answer 2

Answer :

x² + y² = 3.

Explanation :

First find out the distance.

Give points are A(3,0) and B(-3,0).

Let the point be (x,y)

Distance AB = √(-3 - 3)²

                    = √(-6)²

                   = 6.

Then, AB = 6.

Now,

Sum of the squares is four times the distance between A and B.

=> [(x - 3)² + y²] + [(x + 3)² + y²] = 4AB

=> x² + 9 - 6x + y² + x² + 9 + 6x + y² = 4(6)

=> 2x² + 2y² + 18 = 24

=> 2x² + 2y² = 6

=> x² + y² = 3

Therefore, Locus of a point is x² + y² = 3.

Hope it help!