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Question

Find the point on the y-axis which is equidistant from A (3, - 4) and B (- 5, 9).


A

(0,8128)

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B

(0,3)

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C

(0,8126)

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D

(0,10526)

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Solution

The correct option is C

(0,8126)


We have to find a point on the y-axis. Therefore, its x-coordinate will be 0.
Let the point on y-axis be P (0,y)

Distance PA = Distance between (0,y) and (3,4)=(03)2+(y(4))2=(3)2+(y+4)2

Distance PB = Distance between (0,y) and (5,9)=(0(5))2+(y9)2=52+(y9)2

By the given condition, PA = PB, thus
(3)2+(y+4)2=52+(y9)2

Squaring on both sides of the equation

(y+4)2+9=(y9)2+25

y2+16+8y+9=y218y+81+25

26y=10625

26y=81

y=8126

The required point is (0,8126).


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