Question

The straight line ax + by + c = 0 and the co-ordinate axes form an isosceles triangle under which of the following conditions ?

(a) | a | = | b | 

(b) | a | = | c | 

(c) | b | = | c | 

(d) None of these

Answer 1

(a) | a | = | b | 

The equation of line AB, i.e., ax + by + c = 0 in intercept form is ax + by = – c

⇒ \(\frac{x}{\big(-\frac{c}{a}\big)}\) + \(\frac{x}{\big(-\frac{c}{b}\big)}\) = 1

Δ AOB is isosceles Δ if OA = OB, i.e., x-intercept = y – intercept

⇒ \(\frac{-c}{a}\) = \(\frac{-c}{a}\) ⇒ \(\frac{1}{a}\) = \(\frac{1}{a}\) ⇒ | a | = | b |.