A point (2, y) lies on the unit circle such that r=-1. What is the y-coordinate for this point?
The equation for a point on the unit circle is given by x^2 + y^2 = 1. Since the x-coordinate is 2 and the radius is -1, we can substitute these values into the equation:
(2)^2 + y^2 = 1
4 + y^2 = 1
y^2 = -3
Since the square of any real number cannot be negative, there are no real solutions for y.
The equation of a unit circle with center (0,0) is x^2 + y^2 = 1.
Given that the point (2, y) lies on the unit circle, we can substitute the x-coordinate (2) into the equation:
(2)^2 + y^2 = 1
4 + y^2 = 1
To solve for y, we subtract 4 from both sides of the equation:
y^2 = 1 - 4
y^2 = -3
Since we are given that r = -1, the y-coordinate should have a negative value. However, the square root of a negative number is not a real number, so there is no real-valued solution for y in this case.
To find the y-coordinate for a point (2, y) on the unit circle with r = -1, we can use the Pythagorean theorem.
The Pythagorean theorem states that for any point (x, y) on the unit circle, the equation x^2 + y^2 = 1 will always hold true.
In this case, we have x = 2 and r = -1. Let's substitute these values into the equation:
(2)^2 + y^2 = (-1)^2
4 + y^2 = 1
Rearranging the equation, we get:
y^2 = 1 - 4
y^2 = -3
Since square roots of negative numbers are not defined in the real number system, it means there is no real solution for y in this case. Therefore, there is no y-coordinate for the point (2, y) when r = -1 on the unit circle.