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