The locus of the centre of the circles which touch the lines $6 x - 8 y + 5 = 0$ and $6 x - 8 y + 13 = 0$ is $6 x - 8 y + k = 0$ then the value of k is

10

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12

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13

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9

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Solution

The correct option is D $9$
$6 x - 8 y + k = 0$

$\Rightarrow \frac{(k - 5)}{10} = \frac{13 - k}{10}$

$\Rightarrow 2 k = 18$

$∴ k = 9$

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The distance between the lines 6x – 8y + 20 = 0 and 6x – 8y + k = 0 is 1/5, so what are the possible values of K?

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