Question

If the straight line $ax+cy=2b$, where $a,b,c>0$, makes a triangle of area $2$ sq. units with coordinate axes, then

• A. $a,b,c$ are in G.P.
• B. $a,-b,c$ are in G.P.
• C. $a,2b,c$ are in G.P.
• D. $a,-2b,c$ are in G.P.

Answer 1

Answer: (A)

$a,b,c$ are in G.P.

$ax+cy=2b$ can be re-written as

$\frac{x}{\frac{2b}{a}}+\frac{y}{\frac{2b}{c}}=1$

Thus intercepts on the co-ordinate axes are

$x-intercept=\frac{2b}{a}$ and $y-intercept=\frac{2b}{c}$

Since it is a right angled triangle, hence the area of the triangle will be

$=\frac{1}{2}\frac{2b\times 2b}{ac}$

$=2sq.units$

Therefore

$\frac{2b^2}{ac}=2$

$b^2=ac$

Hence a G.P.