Q20 of 47 Page 1

Find a point P on the y-axis which is equidistant from the points A (4, 8) and B (-6, 6). Also, find the distance AP.

Let the co-ordinate of P be (0, y)

Distance between two points is given by,


=


⸫ AP =


⸫ BP =


According to the question,


AP = BP


⇒ =


Squaring both sides,


⇒ 16 + 64 + y2 – 16y = 36 + 36 + y2 – 12y


⇒ 4y = 8


⸫ y = 2


⸫ P = (0, 2)


⸫ AP =


= sq. units


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