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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+27+31y-120=0`

Text Solution

Verified by Experts

The eqation of chord of contact AB is `(3x)/(9)+(4y)/(4)=1 or (x)/(3)+y=1n or +3y-3=0`
Thus, equation of locus of the point whose distances from the point P and the line AB are equal is `(x-3)^(2)+(y-4)^(2)=((x+3y-3)^(2))/(10)`
`or 9x^(2)+y^(2)-6xy-54x-62y+241=0`
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