Q. 195.0( 2 Votes )

If the point <spa

Answer :


Given, PA = PB


Squaring on both sides, we get


PA2 = PB2


We know that the distance between P(x1, y1 ) and Q(x2, y2 ) is .


(-2 – 2)2 + (k – 2)2 = (-2k – 2)2 + (-3 – 2)2


16 + k2 + 4 – 4k = 4k2 + 4 + 8k + 25


16 + k2 + 4 – 4k - 4k2 - 4 - 8k – 25 = 0


-3k2 – 12k – 9 = 0


Dividing by -3, we get


k2 + 4k + 3 = 0


By factorization method,


k2 + k + 3k + 3 = 0


k(k + 1) + 3(k + 1) = 0


(k + 1) (k + 3) = 0


k + 1 = 0 (or) k + 3 = 0


k = -1 (or) k = -3


Now, AP =


AP =


Case 1: When k = -1


AP =


=


√25


AP = 5 units


Case 2: When k = -3


AP =


=


AP = √41 units


The value of k is -1 (or) -3 and the length of AP is 5 units (or) √41 units respectively.


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