Question

Find k such that the line x – 2y + k = 0 touches the circle x² + y² + 3x – 2y + 2 = 0.

Answer 1

Here centre (-\(\frac{3}{2}\), 1), r = \(\sqrt{\frac{9}{4} + 1 - 2}\) = \(\frac{5}{4}\)

r = length of perpendicular from \((-\frac{3}{2}, - 1)\) to the line x – 2y + k = 0