First slide

Equation of line in Straight lines

Question

$Consider the points A (0, 1) and B (2, 0), and P be a point on the line 4 x + 3 y + 9 = 0 . The coordinates of P such that$ $| P A - P B | is maximum are$

Moderate

A

$(- \frac{12}{5}, \frac{17}{5})$
B

$(- \frac{84}{5}, \frac{13}{5})$
C

$(- \frac{6}{5}, \frac{17}{5})$
D

$(0, - 3)$

Solution

The equation of AB is $\frac{x}{2} + \frac{y}{1} = 1$
$or x + 2 y - 2 = 0$
$| P A - P B | \leq A B$

the points l, B, and P are collinear
$Hence, solving x + 2 y - 2 = 0 and 4 x + 3 y + 9 = 0, we get point P \equiv$ $(- \frac{84}{5}, \frac{13}{5})$

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