COMEDK · Maths · 12. Circle
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
- A Inside \(c_1\) only
- B Inside \(c_1\) and \(c_2\)
- C Inside \(c_2\) only
- D Outside \(c_1\) and \(c_2\)
Answer & Solution
Correct Answer
(D) Outside \(c_1\) and \(c_2\)
Step-by-step Solution
Detailed explanation
\(c_1(1,0)=1^2+0^2-2(1)+\dot{4}(0)+5\) \(=1-2+5=4\gt0\) \(\therefore(1,0)\) lies outside of \(c_1\) \(\begin{aligned} c_2(1,0) & =1^2+0^2-1+2 \\ & =1-1+2=2\gt0 \end{aligned}\) \(\therefore(1,0)\) lies outside of \(c_2\)
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