Q70 / 180 · COMEDK 2024 (Memory Based) · Mathematics
If $c_1 \equiv x^2+y^2-2 x+4 y+5=0$ and $c_2 \equiv x^2+y^2-x+2=0$ are two circles. Then the point $(1,0)$ lies
- AInside $c_1$ only
- BInside $c_1$ and $c_2$
- CInside $c_2$ only
- Correct answerDOutside $c_1$ and $c_2$
Solution
$c_1(1,0)=1^2+0^2-2(1)+\dot{4}(0)+5$
$=1-2+5=4\gt0$
$\therefore(1,0)$ lies outside of $c_1$
$\begin{aligned}<br/>c_2(1,0) & =1^2+0^2-1+2 \\<br/>& =1-1+2=2\gt0<br/>\end{aligned}$
$\therefore(1,0)$ lies outside of $c_2$
$=1-2+5=4\gt0$
$\therefore(1,0)$ lies outside of $c_1$
$\begin{aligned}<br/>c_2(1,0) & =1^2+0^2-1+2 \\<br/>& =1-1+2=2\gt0<br/>\end{aligned}$
$\therefore(1,0)$ lies outside of $c_2$
Hence, the correct answer is option: 'D'.