a) To determine whether the point A(2, 6) lies on the circle defined by x^2 + y^2 = 40, we can substitute the x and y coordinates of A into the equation and check if the equation holds true.
Substituting x = 2 and y = 6 into the equation,
2^2 + 6^2 = 40
4 + 36 = 40
40 = 40
The equation holds true, so the point A(2, 6) lies on the circle defined by x^2 + y^2 = 40.
b) To find the equation for the radius from the origin O to point A, we can use the distance formula. The distance between two points (x1, y1) and (x2, y2) is given by:
Distance = √((x2 - x1)^2 + (y2 - y1)^2)
In this case, the origin O is the point (0, 0) and point A is (2, 6). Substituting these values into the distance formula,
Distance = √((2 - 0)^2 + (6 - 0)^2)
= √(2^2 + 6^2)
= √(4 + 36)
= √40
Therefore, the equation for the radius from the origin O to point A is √40.
3. a) Determine whether the point A(2, 6) lies on the circle defined by
x2+ y2 = 40.
b) Find an equation for the radius from the origin O to point A.
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