Question

If a circle whose centre is $(10,0)$ and radius is ' $r$ ' cuts the parabola $y^2=4 x$ at 4 distinct points then minimum value of $[r]$ is
[Note: [k] denotes greatest integer less than or equal to $k$.]

• A. 5
• B. 6
• C. 7
• D. 10

Answer 1

Answer: (B)

$( x -10)^2+ y ^2= r ^2 \& y ^2=4 x$
$(x-10)^2+4 x=r^2$
$x^2-16 x+100-r^2=0$. Both roots of the equation are positive and distinct.
$D >0 \Rightarrow(16)^2-4\left(100- r ^2\right)>0$
$ \Rightarrow 256-400+4 r ^2>0 $
$\Rightarrow r ^2>36 \Rightarrow r >6$
Also, $r<10$. So $r \in(6,10)$.