First slide

Equation of line in Straight lines

Question

A line is drawn perpendicular to line y = 5x, meeting the coordinate axes at A and B. If the area of triangle OAB is 10 sq. units, where O is the origin, then the equation of drawn line is

Moderate

A

$x + 5 y = 10$
B

$x - 5 y = 10$
C

$x + 4 y = 10$
D

$x - 4 y = 10$

Solution

Let the equation of line be
$\frac{x}{a} + \frac{y}{b} = 1$
$A B is perpendicular to y = 5 x . Hence,$ $- \frac{b}{a} \times 5 = - 1 or 5 b = a$
$Area of Δ O A B = \frac{1}{2} | a b |$
$\begin{array}{l} or 10 = \frac{1}{2} |5 b^{2}| \\ or b^{2} = 4 or b = \pm 2, a = \pm 10 \end{array}$
The line can be
$\frac{x}{10} + \frac{y}{2} = 1 or \frac{x}{10} + \frac{y}{2} = - 1$

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