Question

The line segment joining points$(4,7)$and $(-2,-1)$is the diameter of a circle. If the circle intersects the $X-$axis at$A$ and$B$, then$AB$ is equal to

• A. $4$
• B. $5$
• C. $6$
• D. $8$

Answer 1

The correct option is D

$8$

Find the length of the given line segment

Equation of the circle in two point form $=(x–4)(x+2)+(y-7)(y+1)=0$

Since, it cuts $X-$axis, $y=0$

$\Rightarrow x^2–2x–8–7=0$

$\Rightarrow x^2–2x–15=0$

$\Rightarrow (x-5)(x+3)=0$

$x=5,x=-3$

The points are $(5,0)$and$(-3,0)$

$\because AB=5+3=8units$

Hence the correct option is $D$, $8$.