If $A(2,3)$ and $B(2,-3)$ are two points, then the equation of the locus of a point $\mathrm{P}$ such that $\mathrm{PA}+\mathrm{PB}=8$ is

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Aicharya · Accepted Answer

Let co-ordinate of point $\mathrm{P}$ is $(\mathrm{x}, \mathrm{y})$ Now, $\mathrm{PA}+\mathrm{PB}=8$ $\begin{aligned} & \Rightarrow \sqrt{(x-2)^2+(y-3)^2}+\sqrt{(x-2)^2+(y+3)^2}=8 \ & \Rightarrow \sqrt{(x-2)^2+(y-3)^2}=8-\sqrt{(x-2)^2+(y+3)^2} \ & \Rightarrow(x-2)^2+(y-3)^2=64+(x-2)^2+(y+3)^2 \ & -16 \sqrt{(x-2)^2+(y+3)^2} \ & \Rightarrow 4 \sqrt{(x-2)^2+(y+3)^2}=16+3 y \ & \Rightarrow 16\left(x^2+4-4 x+y^2+9+6 yight)=256+9 y^2+96 y \ & \Rightarrow 16 x^2+7 y^2-64 x-48=0\end{aligned}$

If $A(2,3)$ and $B(2,-3)$ are two points, then the equation of the locus of a point $\mathrm{P}$ such that…

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