A family of linear functions is given byfx=1+cx+3 where c∈R. If a member of this family meets a unit circle centred at origin in two coincident points, then ‘c’ can be equal to

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A family of linear functions is given by $f (x) = 1 + c (x + 3)$ where $c \in R$ . If a member of this family meets a unit circle centred at origin in two coincident points, then ‘c’ can be equal to

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$0$

$\frac{3}{4}$

$1$

$\frac{- 3}{4}$

answer is A, B.

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Detailed Solution

The line $y = 1 + c (x + 3)$ is a tangent is the circle $x^{2} + y^{2} = 1 \Rightarrow r = d \Rightarrow c = 0$ or $- \frac{3}{4}$

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