Question

The circle x² + y² = 4x + 8y + 5 intersects the line 3x – 4y = m at two distinct points if

(a) –85 < m < –35 

(b) –35 < m < 15

(c) 15 < m < 65 

(d) 35 < m < 85

Answer 1

(b) : The circle is x² + y² – 4x – 8y – 5 = 0
⇒ (x – 2)² + (y – 4)2 = 52
Length of perpendicular from centre (2, 4) on the line 3x – 4y – m = 0 should be less than radius.