Question

A straight line $\frac{x}{a}-\frac{y}{b}=1$ passes through the point (8, 6) and cuts off a triangle of area 12 units from the axes of coordinates. Find the equations of the straight line.

• A. 3x - 2y = 12
• B. 4x - 3y =12
• C. 3x - 8y + 24 = 0
• D. both (a) and (c)

Answer 1

The correct option is D

both (a) and (c)

We have $\frac{x}{a}-\frac{y}{b}=1$ ....(1)
Since (1) passes through the point (8,6)
$\therefore \frac{8}{a}-\frac{6}{b}=1$....(2)
The line (1) meets the x-axis at the point given by y = 0 and from (1) x =a i.e., the line (1) meets the x-axis at the point A(a,0)
Similarly, the lines meets the y-axis (x=0) at the point B(0, -b).
By the given condition, area of $\Delta =12$
$\Rightarrow \frac{1}{2}ab=12$
$\Rightarrow$ ab=24 $\Rightarrow b=\frac{24}{a}$
Substituting b = $\frac{24}{a}$ in (2), we get
$\frac{8}{a}=\frac{6}{\frac{24}{a}}=1\Rightarrow$ a=4 or-8 and b=6 or -3
Hence, from (1) the equation of the straight line are
$\frac{x}{4}-\frac{y}{6}=1$ and $\frac{x}{-8}-\frac{y}{-3}=1$
$\Rightarrow$ 3x-2y= 12 and 3x-8y+24=0