Question

If $a,c,b$ are in GP, then the line $ax+by+c=0$

• A. has a fixed direction
• B. always passes through a fixed point
• C. forms a triangle with the axes whose area is constant
• D. always cuts intercepts on the axes such that their sum is zero

Answer 1

Answer: (C)

forms a triangle with the axes whose area is constant

Since $a,b,c$ are in G.P
Therefore $c^2=ab$
The area of triangle is
$=\frac{1}{2}\times (-\frac{c}{a})\times (-\frac{c}{b})=\frac{c^2}{2ab}=\frac{1}{2}$