Question

The locus of the point whose ratio of distance from the origin to its distance from $(-2,-3)$ is $5:7$, is given by______

• A. $24\left(x^2+y^2\right)-100x-150y-325=0$
• B. $24\left(x^2+y^2\right)+100x+150y-325=0$
• C. $24\left(x^2+y^2\right)-100x+150y+325=0$
• D. $2x^2+2y^2=325$

Answer 1

Answer: (A)

Let the point $P(x,y)$, such that $OP:AP=5:7$,
where $O$ is the origin and $A(-2,-3),$ so
$\frac{\sqrt{x^2+y^2}}{\sqrt{(x+2{)}^2+(y+3{)}^2}}=\frac{5}{7}$
$\Rightarrow 49\left(x^2+y^2\right)=25\left[x^2+y^2+4x+6y+13\right]$
$\Rightarrow 24\left(x^2+y^2\right)-100x-150y-375=0$