Minimum distance between any two points P _{1} and P _{2} while considering point P _{1} on one circ

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10-1.Circle and System of Circles

hard

The minimum distance between any two points $P _{1}$ and $P _{2}$ while considering point $P _{1}$ on one circle and point $P _{2}$ on the other circle for the given circles' equations

$x^{2}+y^{2}-10 x-10 y+41=0$

$x^{2}+y^{2}-24 x-10 y+160=0$ is .........

A

$4$

B

$3$

C

$2$

D

$1$

(JEE MAIN-2021)

Solution

Given $C_{1}(5,5), r_{1}=3$ and $C_{2}(12,5), r_{2}=3$

Now, $C_{1} C_{2}>r_{1}+r_{2}$

Thus, $\left(P_{1} P_{2}\right)_{\min }=7-6=1$

Standard 11

Mathematics

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