Question

The condition to be imposed on $\beta$ so that $(0,\beta )$ lies on inside the triangle having sides $y+3x+2=0,3y-2x-5=0$ and $4y+x-14=0$ is

• A. $0<\beta <\frac{5}{3}$
• B. $0<\beta <\frac{7}{2}$
• C. $\frac{5}{3}\le \beta \le \frac{7}{2}$
• D. None of these

Answer 1

Answer: (C)

$\frac{5}{3}\le \beta \le \frac{7}{2}$

Clearly point $(0,\beta )$ lies on y-axis

Drawing the graph of the three straight lines, we see that

$Q\equiv (0,\frac{7}{2})$ and

$P\equiv (0,\frac{5}{3})$

Therefore, the point $(0,\beta )$ lies on or inside $△ABC$, when $\frac{5}{3}\le \beta \le \frac{7}{2}$