JEE MAIN - Mathematics (2019 - 10th April Evening Slot - No. 11)
Lines are drawn parallel to the line 4x – 3y + 2 = 0, at a distance
$${3 \over 5}$$
from the origin. Then which one of the
following points lies on any of these lines ?
$$\left( {{1 \over 4}, - {1 \over 3}} \right)$$
$$\left( { - {1 \over 4},{2 \over 3}} \right)$$
$$\left( { - {1 \over 4}, - {2 \over 3}} \right)$$
$$\left( {{1 \over 4},{1 \over 3}} \right)$$
Explanation
Line parallel to 4x – 3y + 2 = 0
is given as 4x – 3y + $$\lambda $$ = 0
distance from origin is
$$\left| {{\lambda \over 5}} \right| = {3 \over 5}$$
$$ \Rightarrow \lambda = \pm 3$$
$$ \therefore $$ required lines are 4x – 3y + 3 = 0 & 4x – 3y – 3 = 0
By Putting $$\left( { - {1 \over 4},{2 \over 3}} \right)$$ on both lines it satisfy.
is given as 4x – 3y + $$\lambda $$ = 0
distance from origin is
$$\left| {{\lambda \over 5}} \right| = {3 \over 5}$$
$$ \Rightarrow \lambda = \pm 3$$
$$ \therefore $$ required lines are 4x – 3y + 3 = 0 & 4x – 3y – 3 = 0
By Putting $$\left( { - {1 \over 4},{2 \over 3}} \right)$$ on both lines it satisfy.
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