Answer:
a = -√3/3
b = 2√3/3
Explanation:
Finding the slope of the tangent at C by finding the derivative:
x^2 + y^2 = 1
2x + 2y y' = 0
2y y' = -2x
y' = -2x / 2y = -x/y
So the slope = - 1/2 / √3/2
= -1/2 * 2/√3
= -1/√3
= -√3/3
Using the point-slope form of a straight line
y - y1 = m(x - x1)
y - √3/2 = -√3/3(x - 1/2)
y - √3/2 = -√3/3 x +√3/6
y = -√3/3 x + √3/6 +√3/2
y = -√3/3 x + 4√3/6
y = -√3/3x + 2√3/3