JEE PYQ: Circle Question 14
Question 14 - 2020 (02 Sep Shift 1)
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 ______.
Show Answer
Answer: 9
Solution
Center $(1,2)$, $r = 1$. Distance from center to line $< 1$: $\frac{|3 + 8 - k|}{5} < 1 \Rightarrow |11 - k| < 5 \Rightarrow k \in (6, 16)$. Integral values: $7, 8, 9, 10, 11, 12, 13, 14, 15$ = 9 values.
BETA
