Question

If a circle whose centre is $(10,0)$ and radius is ' $r$ ' cuts the parabola $y^2=4x$ 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)

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