Question

A straight line is drawn through the point P(3, 4) meeting the positive direction of coordinate axes at the points A and B. If O is the origin, then minimum area of ΔOAB is equal to ______.

Options

• 12 sq units

• 6 sq units

• 24 sq units

• 48 sq units

Answer 1

A straight line is drawn through the point P(3, 4) meeting the positive direction of coordinate axes at the points A and B. If O is the origin, then minimum area of ΔOAB is equal to 24 sq units.

Explanation:

Let the equation of drawn line be `x/a + y/b` = 1, where a > 3, b > 4, as the line passes through (3, 4) and meets the positive direction of coordinate axes.

We have, `3/a + 4/b` = 1

`\implies` b = `(4a)/((a - 3))`

Now, the area of ΔAOB,

Δ = `1/2 ab = (2a^2)/(a - 3)`

`\implies (dΔ)/(da) = (2a(a - 6))/((a - 3))`

Clearly, a = 6 is the point of minima for triangle.

Thus, Δ_min = `(2 xx 36)/3` = 24 sq units