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The locus of a point which divides a lin...

The locus of a point which divides a line segment AB=4 cm in 1 : 2, where A lies on the line y=x and B lies on the y=2x is

A

`234x^2 + 153y^2 -378xy -32 = 0`

B

`234x^2 + 153y^2 - 378xy + 32 = 0`

C

`234x^2 + 153y^2 + 378xy + 32 = 0`

D

None of these

Text Solution

Verified by Experts

The correct Answer is:
A

`3h = t_2 + 2t_1`
`3k = 2t_2 + 2t_1`
`t_2 = 3k - 3h`
`3h = 3k -3h + 2t_1`
`(6h - 3k)/(2) = t_1`
`(t_1 - t_2)^2 + (t_1+2t_2)^2 = 16`
`((6h-3k)/(2) - 3k +3h)^2 + ((6h - 3k)/(2) - 6k + 6h)^2 = 16`
`((6h - 3k - 6k + 6h)^2 )/(4) + ((6h- 3k -12k +12h)^2)/(4) = 64`
`(12h -9k)^2 + (18h - 15k)^2 = 64`
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