Question
Question: The range of l, if the line 3x – 4y = l meets the circle x<sup>2</sup> + y<sup>2</sup> –4x –8y – 5 ...
The range of l, if the line 3x – 4y = l meets the circle
x2 + y2 –4x –8y – 5 = 0 in real points-
A
(0, 15)
B
(–35, 15)
C
(–35, 0)
D
None of these
Answer
(–35, 15)
Explanation
Solution
Eliminating y from circle and line
25x2 –2(3l + 80)x + (l2 +32l –80) = 0
for real points
B2 – 4AC > 0. on solving
\ l2 + 20l – 525 < 0 ̃ (l + 35) (l –15) < 0
̃ –35 < l < 15