Locus of the image of point (2,3) in the lin | vedclass

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Question

Let $M$ be mid-point of $B B^{\prime}$ and $A M$ is $\perp$ bisector of $B B^{\prime}$

(where $A$ is the point of intersection of the given lines)

Vedclass · Accepted Answer

circle of radius  $\;\sqrt 2 $

Vedclass · Answer

Let $M$ be mid-point of $B B^{\prime}$ and $A M$ is $\perp$ bisector of $B B^{\prime}$

(where $A$ is the point of intersection of the given lines)

$(x-2)(x-1)+(y-2)(y-3)=0$

$\Rightarrow\left(\frac{h+2}{2}-2\right)\left(\frac{h+2}{2}-1\right)+\left(\frac{k+3}{2}-2\right)\left(\frac{k+3}{2}-3\right)=0$

$\Rightarrow(h-2)(h)+(k-1)(k-3)=0$

$\Rightarrow \quad x^{2}-2 x+y^{2}-4 y+3=0$

$\Rightarrow \quad(x-1)^{2}+(y-2)^{2}=2$

Locus of the image of point $ (2,3)$ in the line $\left( {2x - 3y + 4} \right) + k\left( {x - 2y + 3} \right) = 0,k \in R$ is a:

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