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Tangents are drawn from the point P(3,4)...

Tangents are drawn from the point P(3,4) to the ellipse `x^(2)/9+y^(2)/4=1` touching the ellipse at point A and B. Q. The equation of the locus of the points whose distance from the point P and the line AB are equal, is

A

`9x^(2)+y^(2)-6xy-54x-62y+241=0`

B

`x^(2)+9y^(2)+6xy-54x+62y-241=0`

C

`9x^(2)+9y^(2)-6xy-54x-62y-241=0`

D

`x^(2)+y^(2)-2xy+27x+31y-120=0`

Text Solution

Verified by Experts

The correct Answer is:
A
The equation AB is `x//3+y=1orx+3y-3=0`. The locus of the point is given by
`sqrt((x-3)^(2)+(y-4)^(2))=|(x+3y-3)/(sqrt(1+9))|`
or , `9x^(2)+y^(2)-6xy-54x-62y+241=0`
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