Question

Two circles have the equations $x^2+y^2-4x-6y-8=0$ and $x^2+y^2-2x--3=0$. Then

• A. they cut each other
• B. they touch each other
• C. one circle lies inside the other
• D. one circle lies wholly outside the other

Answer 1

The correct option is A they cut each other

$C1(2,3)$ and $r_1=\sqrt{2^2+3^2+8}=\sqrt{21}$
$C2(1,0)$ and $r_2=\sqrt{1^2+3}=2$
$C1C2=\sqrt{1}0$ and $r_1+r_2=\sqrt{2}1+2$
Since, $C1C2<r_1+r_2$
Therefore, two circles intersect each other
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