Consider the lines , being a parameter, all passing through a point P. One of these lines (say L) is farthest from the origin. If the distance of L from the point (3, 6) is d, then the value of is [2025]

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Solution

Q.
Consider the lines $x (3 λ + 1) + y (7 λ + 2) = 17 λ + 5$ , $λ$ being a parameter, all passing through a point P. One of these lines (say L) is farthest from the origin. If the distance of L from the point (3, 6) is d, then the value of $d^{2}$ is [2025]

1 15

2 10

3 30

4 20

Ans.
(4)

We have, $x (3 λ + 1) + y (7 λ + 2) = 17 λ + 5$

$\Rightarrow (x + 2 y - 5) + λ (3 x + 7 y - 17) = 0$

The intersection of family of lines is the point P(1, 2) and let $Q \equiv (3, 6)$ .

Now, $d = P Q = \sqrt{2^{2} + 4^{2}} = \sqrt{20} \Rightarrow d^{2} = 20$

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