Question

The straight line `ax+by+c=0` and the coordinate axes form an isosceles triangle under which one of the following consitions ?
A. `|a|=|b|`
B. `|a|=|c|`
C. `|b|=|c|`
D. none of these

Answer 1

Correct Answer - A
Co-ordinate axes and straight line `ax+by+c=0` form an isosceles triangle. This is possible when, the line makes equal intercept on both the axes.

Expressing `ax+by+c=0` in intercept form :
`ax+by=-c or x/(-c/a)+y/(-c/b)=1`
So, x-inntercept `=-c/a` and y-intercept `=-c/b`
Since, `-c/a=-c/b`
Hence, `a=b`
Intercepts can be on both the sides of axis.
So, `|a|=|b|`