Question

Assertion ($A$) The equation to the locus of points which are equidistant from the points$(-3,2)$, $(0,4)$ is $6x+4y-3=0$
Reason ($R$) The locus of points which are equidistant to $A,B$ is perpendicular bisector of $AB$

• A. $A$ true, $R$ true and $R$ is correct explanation of $A$.
• B. $A$ true, $R$ true but $R$ is not correct explanation $A$.
• C. $A$ true, $R$ false
• D. $A$ false, $R$ true

Answer 1

The correct option is A $A$ true, $R$ true and $R$ is correct explanation of $A$.

Let $(h,k)$ be the points which are equidistant from point $(-3,2)$ and $(0,4)$

Then equation of the locus of points is given by

$(h+3{)}^2+(k-2{)}^2=(h-0{)}^2+(k-4{)}^2$

$⟹h^2+6h+9+k^2-4k+4=h^2+k^2-8k+16$
$⟹6h+4k-3=0$
$\therefore 6x+4y-3=0$
This is the perpendicular bisector of the line joining $(-3,2)$ and $(0,4)$

Hence, both $A$ and $R$ are true and $R$ is correct explanation of $A$.