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Is the point $(0,4)$ inside or outside the circle of radius $4$ with centre at $(-3,1)$ ?

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Positive and negative square roots

Full solution

Q. Is the point

(0,4)

inside or outside the circle of radius

4

with centre at

(-3,1)

?

Calculate Distance Formula: To determine if the point is inside or outside the circle, we'll use the distance formula to find the distance from the point to the center of the circle: $d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$ , where $(x_1, y_1)$ is the center of the circle and $(x_2, y_2)$ is the point in question.
Plug in Values: Plug in the values: $d = \sqrt{(0 - (-3))^2 + (4 - 1)^2} = \sqrt{(3)^2 + (3)^2}.$
Calculate Distance: Calculate the distance: $d = \sqrt{9 + 9} = \sqrt{18}.$
Compare to Radius: Compare the distance to the radius of the circle. If the distance is less than the radius, the point is inside the circle. If it's equal, the point is on the circle, and if it's more, the point is outside the circle.
Final Result: Since $\sqrt{18}$ is approximately $4.24$ , which is greater than the radius of the circle ( $4$ ), the point $(0,4)$ is outside the circle.

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