First slide

Equation of line in Straight lines

Question

A straight line L with negative slope passes through the point (8,2) and cuts the positive coordinate axes at points P and Q. The absolute minimum value of OP + OQ as L varies, where O is the origin, is

Moderate

Solution

Let the equation of line be (y -2) - m(x - 8) where m <0
$\begin{aligned} \Rightarrow P \equiv (8 - \frac{2}{m}, 0) and Q \equiv (0, 2 - 8 m) \\ Now, OP + OQ & = | 8 - \frac{2}{m} | + | 2 - 8 m | \\ = 10 + \frac{2}{- m} + (- 8 m) \\ \geq 10 + 2 \sqrt{\frac{2}{- m} \times (- 8 m)} \geq 18 \end{aligned}$

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