Question:
The number of integral values of $k$ for which the line, $3 x+4 y=k$ intersects the circle, $x^{2}+y^{2}-2 x-4 y+4=0$ at two distinct points is_________.
Solution:
The given circle is $x^{2}+y^{2}-2 x-4 y+4=0$
$\therefore$ Centre of circle $(1,2), r=1$.
If line cuts circle then $p $\Rightarrow\left|\frac{3+8-k}{5}\right|<1 \Rightarrow k \in(6,16)$ $k=7,8,9,10,11,12,13,14,15$
Click here to get exam-ready with eSaral
For making your preparation journey smoother of JEE, NEET and Class 8 to 10, grab our app now.