If y = 2√2x + c is a tangent to the circle x2 + y2 =16, find the val

1.	If y = 2√2x + c is a tangent to the circle x2 + y2 =16, find the value of c.
Answer» The condition for the line y = mx + c to be a tangent to the circle x² + y² = a² is c² = a² (1 + m²) Here x² + y² = 16 ⇒ a² = 16 y = 2√2x + c ⇒ m = 2√2 and c = c The condition is c² = a² (1 + m²) (i.e) c² = 16(1 + 8) = 144 ⇒ c = ± 12

If y = 2√2x + c is a tangent to the circle x2 + y2 =16, find the value of c.

Answer»

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

c² = a² (1 + m²)

Here x² + y² = 16 ⇒ a² = 16

y = 2√2x + c ⇒ m = 2√2 and c = c

The condition is c² = a² (1 + m²)

(i.e) c² = 16(1 + 8) = 144

⇒ c = ± 12