The number of integral values of k for which the line 3x+4y=k intersects the circle x^2+y^…

Question

The number of integral values of $k$ for which the line $3x+4y=k$ intersects the circle $x^2+y^2-2x-4y+4=0$ at two distinct points is \_\_\_\_\_\_\_\_.

Answer: 9

Accepted Answer

Centre $(1,2)$, $r=1$. Two distinct points: $\dfrac{|3+8-k|}5<1\Rightarrow|11-k|<5\Rightarrow6<k<16$.

Integers: $7,8,\dots,15$ --- $9$ values.

Solutions · 1