Final answer:
To find the equations of the lines passing through the origin and tangent to a circle with radius 2 and center at point (2,1), we need to find the points of tangency. This can be done by finding the slopes of the radius lines from the origin to the circle's center, and then using those slopes to find the equations of the tangent lines using point-slope form.
Step-by-step explanation:
To find the equations of the lines passing through the origin and tangent to a circle with radius 2 and center at point (2,1), we need to find the points of tangency. This can be done by finding the slopes of the radius lines from the origin to the circle's center, and then using those slopes to find the equations of the tangent lines using point-slope form.
The slope of the radius line is given by the formula: slope = (y2 - y1) / (x2 - x1). Substituting the given values, we get: slope = (1 - 0) / (2 - 0) = 1/2.
Now, we can find the equations of the tangent lines using point-slope form: y - y1 = slope(x - x1). Substituting the values of (x1, y1) = (2, 1) and slope = 1/2, we get two equations: y - 1 = (1/2)(x - 2) and y - 1 = -(1/2)(x - 2).