Find the maximum distance of the point \(K(10,7)\) from the circle \(x^2+y^2-4 x-2 y-20=0\)
Find the maximum distance of the point \(K(10,7)\) from the circle \(x^2+y^2-4 x-2 y-20=0\)
25
10
15
5
Solution
Equation of given circle is
\(\begin{aligned}
& x^2+y^2-4 x-2 y-20 & =0 \\
\Rightarrow & (x-2)^2+(y-1)^2 & =25
\end{aligned}\)
Having centre \(C(2,1)\) and radius \(r=5\)
\(\therefore\) The maximum distance of the point \(K(10,7)\) from the given circle is \(C K+r\)
\(\begin{aligned}
& =\sqrt{(10-2)^2+(7-1)^2}+5 \\
& =\sqrt{64+36}+5=10+5=15 \text { unit }
\end{aligned}\)
Hence, option (c) is correct.