The number of integers in the range of m for | vedclass

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(A) Let the circle be $S: x^2 + y^2 - 3x + 1 = 0$ and the line be $L: 2x - y - 2 = 0$.For the point $(m, 1)$ to lie inside the circle,$S(m, 1) < 0$:$m

Vedclass · Accepted Answer

$0$

Vedclass · Answer

(A) Let the circle be $S: x^2 + y^2 - 3x + 1 = 0$ and the line be $L: 2x - y - 2 = 0$.For the point $(m, 1)$ to lie inside the circle,$S(m, 1) $m^2 + 1^2 - 3m + 1 For the point $(m, 1)$ to lie on the same side of the line $L$ as the center of the circle,we check the sign of $L(m, 1)$ relative to the center $(1.5, 0)$:$L(1.5, 0) = 2(1.5) - 0 - 2 = 1 > 0$.Thus,we require $L(m, 1) $2m - 1 - 2 Combining $m \in (1, 2)$ and $m There are no integers in the interval $(1, 1.5)$.Therefore,the number of integers is $0$.

The number of integers in the range of $m$ for which the point $(m, 1)$ lies in the smaller region enclosed by the circle $x^2 + y^2 - 3x + 1 = 0$ and the line $2x - y = 2$ is

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