A line passes through a point A (1, 2) and makes an angle of 600 with the x–axis and intercepts the line x + y = 6 at the point P. Find AP.

Home » A line passes through a point A (1, 2) and makes an angle of 600 with the x–axis and intercepts the line x + y = 6 at the point P. Find AP.

A line passes through a point A (1, 2) and makes an angle of 600 with the x–axis and intercepts the line x + y = 6 at the point P. Find AP.

Given:

$\left( {{x}_{1}},\text{ }{{y}_{1}} \right)\text{ }=\text{ }A\text{ }\left( 1,\text{ }2 \right),\text{ }\theta ~=\text{ }60{}^\circ$

To find the distance AP,

On using the formula,

The equation of the line is given by:

RD Sharma Solutions for Class 11 Maths Chapter 23 – The Straight Lines - image 28

Here, r represents the distance of any point on the line from point

$:A\text{ }\left( 1,\text{ }2 \right).$

The coordinate of any point P on this line are:

$~\left( 1\text{ }+\text{ }r/2,\text{ }2\text{ }+\text{ }\surd 3r/2 \right)~$

Now , P lies on the line:

$x\text{ }+\text{ }y\text{ }=\text{ }6$

hence ,

RD Sharma Solutions for Class 11 Maths Chapter 23 – The Straight Lines - image 29

∴ The value of AP is

$:\text{ }3\left( \surd 3\text{ }\text{ }1 \right)$

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