The circles x^2 + y^2 - 10x + 16 = 0 and x^2 | vedclass

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(C) For the first circle $x^2 + y^2 - 10x + 16 = 0$,the center $C_1 = (5, 0)$ and radius $r_1 = \sqrt{5^2 - 16} = \sqrt{25 - 16} = \sqrt{9} = 3$.For t

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$2 < r < 8$

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(C) For the first circle $x^2 + y^2 - 10x + 16 = 0$,the center $C_1 = (5, 0)$ and radius $r_1 = \sqrt{5^2 - 16} = \sqrt{25 - 16} = \sqrt{9} = 3$.For the second circle $x^2 + y^2 = r^2$,the center $C_2 = (0, 0)$ and radius $r_2 = r$.The distance between the centers $d = \sqrt{(5-0)^2 + (0-0)^2} = 5$.Two circles intersect at two distinct points if $|r_1 - r_2| Substituting the values,we get $|3 - r| From $5  2$.From $|3 - r|  -2$.Combining these conditions,we get $2 < r < 8$.

The circles $x^2 + y^2 - 10x + 16 = 0$ and $x^2 + y^2 = r^2$ intersect each other in two distinct points,if

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