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Q.

If the lines $2 x + 3 y - 4 = 0$ and $k x + 4 y - 2 = 0$ are conjugate with respect to the circle $x^{2} + y^{2} = 4$ then
$k - 1 =$

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a

-5

b

-6

c

6

d

5

answer is A.

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Detailed Solution

$r^{2} (l_{1} l_{2} + m_{1} m_{2}) = n_{1} n_{2}$

$4 (2 k + 12) = (- 4) (- 2)$

$2 k + 12 = 2 \Rightarrow 2 k = - 10$

$k = - 5$

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If the lines 2x+3y−4=0 and kx+4y−2=0 are conjugate with respect to the circle x2+y2=4 then k-1=