Answer:
If the point (1,5) lies on a circle with center (0,0), then the radius of the circle is the distance from the center to the point (1,5), which is:
r = sqrt((1-0)^2 + (5-0)^2) = sqrt(26)
So the equation of the circle is:
x^2 + y^2 = 26
To find a point in quadrant 2 that lies on the circle, we need to find a point with a negative x-coordinate and a positive y-coordinate that satisfies this equation.
Among the given options, only (a) (-5,1) and (e) (-2,3) have a negative x-coordinate. Let's check if they satisfy the equation of the circle:
For point (a) (-5,1):
x^2 + y^2 = 26
(-5)^2 + 1^2 = 26
25 + 1 = 26
This point does not lie on the circle.
For point (e) (-2,3):
x^2 + y^2 = 26
(-2)^2 + 3^2 = 26
4 + 9 = 26
This point also does not lie on the circle.
Therefore, among the given options, there is no point in quadrant 2 that lies on the circle.