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Let A=(4, 0), B=(0, 12) be two points in...

Let `A=(4, 0), B=(0, 12)` be two points in the plane. The locus of a point C such that the area of triangle ABC is 18 sq. units is -

A

`(y+3x+12)^(2)=81`

B

`(y+3x+81)^(2)=12`

C

`(y+3x-12)^(2)=81`

D

`(y+3x-81)^(2)=12`

Text Solution

Verified by Experts

The correct Answer is:
C

`1/2|(1,x,y),(1,0,12),(1,4,0)|= pm 18`
`1(-48)-x(-12)+y(4)= pm 36`
`12x+4y-48=pm 36`
`3x+y-12= pm 9`
`(3x+y-12)^(2)=81`
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