Question

Find the length of the chord of the circle x² + y² – 6x + 15y – 16 = 0 intercepted by the x-axis.

Answer 1

Given x² + y² – 6x + 15y – 6 = 0 

C = \((3, \frac{-15}{2})\) & c = -16 

Length intercepted by x – axis = 2\(\sqrt{q^2 - c}\) 

\(= 2\sqrt{(3)^2 - (-16)}\) = 2\(\sqrt{9 + 16}\) = 2√25 = 10

∴ Length = 10 units