Question

Determine whether the point (3,4) lies on the circle with radius 6 and center (-2,3).

Answer 1

The point (3,4) does not lie on the circle.

Step-by-step explanation:

To determine whether the point (3,4) lies on the circle, we can use the distance formula. The distance between the center (-2,3) and the point (3,4) is given by:

d = sqrt((x2 - x1)^2 + (y2 - y1)^2)

Substituting the values, we get:

d = sqrt((3 - (-2))^2 + (4 - 3)^2) = sqrt(25 + 1) = sqrt(26)

Since the distance is not equal to the radius (6), the point (3,4) does not lie on the circle.