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Find those points on the y-axis, each of...

Find those points on the y-axis, each of which is at a distance of 13 units from the point A(-5, 7).

A

`(1,19)`

B

`(2,19)`

C

`(0,19)`

D

`(1,2)`

Text Solution

Verified by Experts

The correct Answer is:
C
Let the required point on the y-axis be P(0, y). Then,
`PA = 13 rArr PA^(2) = 169`
`rArr (0+5)^(2) + (y-7)^(2) = 169`
`rArr y^(2)-14y +74 = 169 rArr y^(2) -14y -95 =0`
`rArr y^(2) - 19y +5y -95=0 rArr y(y-19) +5(y-19) = 0`
`rArr (y-19)(y+5) = 0 rArr y-19 = 0" or "y +5 = 0`
`rArr y = 19 " or "y = -5`
Hence, the required points on the y-axis are B(0, 19) and C(0, -5).
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