Question

A circle is centered at J(3, 3) and has a radius of 12.

Where does the point F(-6,-5) lie?
Choose 1 answer:
A.- Inside the circle
B.-On the circle
C.- Outside the circle

Answer 1

outside the circle

Explanation:

khan

Answer 2

`(-6,\, -5)` is outside the circle of radius of
`12` centered at
`(3,\, 3)`.

Explanation:

Let
`J` and
`r` denote the center and the radius of this circle, respectively. Let
`F` be a point in the plane.

Let
`d(J,\, F)` denote the Euclidean distance between point
`J` and point
`F`.

In other words, if
`J` is at
`(x_j,\, y_j)` while
`F` is at
`(x_f,\, y_f)`, then
`\displaystyle d(J,\, F) = \sqrt{(x_j - x_f)^(2) + (y_j - y_f)^(2)}`.

Point
`F` would be inside this circle if
`d(J,\, F) < r`. (In other words, the distance between
`F\!` and the center of this circle is smaller than the radius of this circle.)

Point
`F` would be on this circle if
`d(J,\, F) = r`. (In other words, the distance between
`F\!` and the center of this circle is exactly equal to the radius of this circle.)

Point
`F` would be outside this circle if
`d(J,\, F) > r`. (In other words, the distance between
`F\!` and the center of this circle exceeds the radius of this circle.)

Calculate the actual distance between
`J` and
`F`:

`\begin{aligned}d(J,\, F) &= \sqrt{(x_j - x_f)^(2) + (y_j - y_f)^(2)}\\ &= \sqrt{(3 - (-6))^(2) + (3 - (-5))^(2)} \\ &= √(145) \end{aligned}`.

On the other hand, notice that the radius of this circle,
`r = 12 = √(144)`, is smaller than
`d(J,\, F)`. Therefore, point
`F` would be outside this circle.