Question

If y = `2sqrt(2)x + "c"` is a tangent to the circle x² + y² = 16, find the value of c

Answer 1

The condition of the line y = mx + c to be a tangent to the circle x² + y² = a² is

c² = a²(1 + m²)

a² = 16

m = `2sqrt(2)`

⇒ m² = 4 × 2 = 8

c² = 16(1 + 8)

c² = 16(9)

c = ± 4 × 3 = ± 12

∴ c = ± 12.