First slide

Equation of line in Straight lines

Question

P is a point on either of the two lines $y - \sqrt{3} |x| = 2$ at a distance of 5 units from their point of intersection. The coordinates of the foot of the perpendicular from P on the bisector of the angle between them are

Moderate

A

$[0, \frac{1}{2} (4 + 5 \sqrt{3})] o r [0, \frac{1}{2} (4 - 5 \sqrt{3})]$ depending on which line the point P is taken
B

$[0, \frac{1}{2} (4 + 5 \sqrt{3})]$
C

$[0, \frac{1}{2} (4 - 5 \sqrt{3})]$
D

$[\frac{5}{2}, \frac{5 \sqrt{3}}{2}]$

Solution

Equation, of two lines are $y = \sqrt{3} x + 2, i f x \geq 0$ and $y = - \sqrt{3} x + 2, i f x \geq 0$
Clearly, $y \geq 2$
Also, y-axis is the bisector of the angle between the two lines. $P_{1}, P_{2}$ are two points on these lines, at a distance 5 units from A.. Q is the foot of the $⊥$ from $P_{1}$ and $P_{2}$ on the bisector (y-axis).
Then, the coordinates of Q are (0, 2 + 5 cos 30º)
$= (0, 2 + \frac{5 \sqrt{3}}{2}) = (0, \frac{1}{2} (4 + 5 \sqrt{3}))$

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