Q. A straight line passing through $P$ (3, 1) meet the coordinate axes at $A$ and $B$. It is given that distance of this straight line from the origin ‘$O$’ is maximum. Area of $\mathrm{\Delta}\ OAB$ is equal to
A) $\frac{50}{3}\ sq\ unit$
B) $\frac{25}{3}\ sq\ unit$
C) $\frac{20}{3}\ sq\ unit$
D) $\frac{100}{6}\ sq\ unit$
Explanation
(a)
Line passing through $P$ farthest from $O$ must be perpendicular to $OP$, so equation is
[image:10_image10.emf]
$y - 1 = - 3(x - 3)$
$\Rightarrow 3x + y = 10$
This line meet the coordinate axes at
${A \equiv \left( \frac{10}{3},\ 0 \right)\ \ and\ B \equiv (0,\ 10)
}{So,\ Area\ of\ \mathrm{\Delta}OAB = \frac{1}{2} \times \frac{10}{3} \times 10 = \frac{50}{3}sq\ unit}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.