Question

Find the locus of a variable point whose distance from $A(4,0)$ is equal to its distance from $B(0,2).$

• A. $6x-3y-10=0$
• B. $2x-y-3=0$
• C. $2x-y+3=0$
• D. $6x+3y+9=0$

Answer 1

The correct option is B $2x-y-3=0$

Let $P$ is the variable point $(x,y)$ whose distance from $A(4,0)$ is equal to its its distance from $B(0,2)$

$\therefore \sqrt{(x-4{)}^2+(y-0{)}^2}=\sqrt{(x-0{)}^2+(y-2{)}^2}$

$\Rightarrow x^2-8x+16+y^2=x^2+y^2-4y+4$

$\Rightarrow -8x+4y+16-4=0$

$\Rightarrow 2x-y-3=0$

Then equation (B) is $2x-y-3=0$ locus of the required point.