Question

The equation of the locus of the point whose distance from the point $P$ and the line $AB$ are equal, is

• A. $x^2+9y^2+6xy-54x+62y-241=0$
• B. $9x^2+9y^2-6xy-54x-62y-241=0$
• C. $x^2+y^2-2x+27x-31y-120=0$
• D. $9x^2+y^2-6xy-54x-62y+241=0$

Answer 1

The correct option is D $9x^2+y^2-6xy-54x-62y+241=0$

Equation of $AB=y-0=-\frac{1}{3}(x-3)$
$x+3y-3=0$
$|x+3y-3{|}^2=10\left[\right(x-3{)}^2+(y-4{)}^2]$
(Look at coefficient of $x^2$ & $y^2$ in the answers)