Find the minimum and maximum distance from th | vedclass

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Question

(A) The given circle is $x^2 + y^2 = 4$,which has center $C = (0, 0)$ and radius $r = 2$.The distance from the point $P(6, 8)$ to the center $C(0, 0)$

Vedclass · Accepted Answer

$8, 12$

Vedclass · Answer

(A) The given circle is $x^2 + y^2 = 4$,which has center $C = (0, 0)$ and radius $r = 2$.The distance from the point $P(6, 8)$ to the center $C(0, 0)$ is given by the distance formula:$d = \sqrt{(6-0)^2 + (8-0)^2} = \sqrt{36 + 64} = \sqrt{100} = 10$.The minimum distance from the point to the circle is $d - r = 10 - 2 = 8$.The maximum distance from the point to the circle is $d + r = 10 + 2 = 12$.Thus,the minimum and maximum distances are $8$ and $12$ respectively.

Find the minimum and maximum distance from the point $(6, 8)$ to the circle $x^2 + y^2 = 4$.

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