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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)=√(0−3)2+(y−(−4))2=√(−3)2+(y+4)2 Distance PB = Distance between (0,y) and (−5,9)=√(0−(−5))2+(y−9)2=√52+(y−9)2 By the given condition, PA = PB, thus √(−3)2+(y+4)2=√52+(y−9)2 Squaring on both sides of the equation ∴ (y+4)2+9=(y−9)2+25 y2+16+8y+9=y2−18y+81+25 26y=106−25 26y=81 y=8126 ∴ The required point is (0,8126).

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