A point moves so that square of its distance from the point $(3, -2)$ is numerically equal to its distance from the line $5x - 12y = 13$. The equation of the locus of the point is
A point moves so that square of its distance from the point $(3, -2)$ is numerically equal to its distance from the line $5x - 12y = 13$. The equation of the locus of the point is
- A
$13{x^2} + 13{y^2} - 83x + 64y + 182 = 0$
- B
${x^2} + {y^2} - 11x + 16y + 26 = 0$
- C
${x^2} + {y^2} - 11x + 16y = 0$
- D
None of these
Similar Questions
If vertices of a parallelogram are respectively $(0, 0)$, $(1, 0)$, $(2, 2)$ and $(1, 2)$, then angle between diagonals is
If vertices of a parallelogram are respectively $(0, 0)$, $(1, 0)$, $(2, 2)$ and $(1, 2)$, then angle between diagonals is
Two sides of a parallelogram are along the lines $4 x+5 y=0$ and $7 x+2 y=0$. If the equation of one of the diagonals of the parallelogram is $11 \mathrm{x}+7 \mathrm{y}=9$, then other diagonal passes through the point:
- [JEE MAIN 2021]
A rod of length eight units moves such that its ends $A$ and $B$ always lie on the lines $x-y+2=0$ and $y+2=0$, respectively. If the locus of the point $P$, that divides the $\operatorname{rod} AB$ internally in the ratio $2: 1$ is $9\left(x^2+\alpha y^2+\beta x y+\gamma x+28 y\right)-76=0$, then $\alpha-\beta-\gamma$ is equal to :
- [JEE MAIN 2025]
In a triangle $ABC,$ side $AB$ has the equation $2 x + 3 y = 29$ and the side $AC$ has the equation , $x + 2 y = 16$ . If the mid - point of $BC$ is $(5, 6)$ then the equation of $BC$ is :
In a triangle $ABC,$ side $AB$ has the equation $2 x + 3 y = 29$ and the side $AC$ has the equation , $x + 2 y = 16$ . If the mid - point of $BC$ is $(5, 6)$ then the equation of $BC$ is :
A point moves such that its distance from the point $(4,\,0)$is half that of its distance from the line $x = 16$. The locus of this point is
A point moves such that its distance from the point $(4,\,0)$is half that of its distance from the line $x = 16$. The locus of this point is