Question

Complete set of values of m, for which point $(m,1)$ lies in smaller segment formed by $x^2+y^2-3x+1=0$ and line $2x-y=2$, is?

• A. $(1,2)$
• B. $\left(\frac{3}{2},2\right)$
• C. $\left(1,\frac{3}{2}\right)$
• D. $(-\infty ,1)\cup (2,\infty )$

Answer 1

The correct option is C $\left(1,\frac{3}{2}\right)$

Circle $x^2+y^2-3x+1\Rightarrow {(x-\frac{3}{2})}^2+y^2=\frac{5}{4}$ and line $2x-y=2$

For $m$ to be in smaller segment from figure

at $y=1$ circle $\in \{1,2\}$

at $y=1$ and line $2x-y=2$ is at $x=\frac{3}{2}$

$m\in (1,\frac{3}{2})$