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Options

A. `-(1)/(r )`
B. `(1)/(r )`
C. `(2)/( r)`
D. `-(2)/(r )`

Answer

C, D

Explanation

Here, coordinate `M = ((t_(1)^(2) + t_(2)^(2))/(2), t_(1) + t_(2))` i.e., mid-point of chord AB.

`MP = t_(1) + t_(2) = r`
Also, `m_(AB) = (2t_(2) - 2t_(1))/(t_(2)^(2) - t_(1)^(2)) = (2)/(t_(2) + t_(1))` [when AB is chord]
`implies m_(AB) = (2)/(r )` [from Eq. (i)]
Also, `m_(AB) = - (2)/(r )` [when A'B' is chord]
Hence, (c,d) are the correct options.