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 $4 x + 3 y + 9 = 0 .$ Then coordinates of P such that $|PA - PB|$ is maximum are

Moderate

A

$(- 12 / 5, 17 / 5)$
B

$(- 24 / 5, 17 / 5)$
C

$(- 6 / 5, 17 / 5)$
D

$(0, - 3)$

Solution

The equation of AB is
$y - 1 = \frac{0 - 1}{2 - 1} x or x + 2 y - 2 = 0$
$|PA - PB| \leq AB$
Thus, $|PA - PB|$ is maximum if the points A,B, and P are collinear.
Hence, solving $x + 2 y - 2 = 0$ and $4 x + 3 y + 9 = 0,$ we get point $P \equiv (- 24 / 5, 17 / 5) .$

Get Instant Solutions

When in doubt download our app. Now available Google Play Store- Doubts App

Recieve an sms with download link

Doubts App

OR

SCAN ME

Doubts App

Doubts App