A circle with center C (4,-2) contains the point D (8,1). what equation of the line perpendicular to the radius of the circle passing through point C?

First, determine the slope of the radius by the equation,

     m = (y₂ - y₁)/ (x₂ - x₁)

Substituting the known values,
    m = (1 - -2)/(8 - 4) = 3/4

If the unknown line is perpendicular to this, the slope should be the negative reciprocal which is equal to -4/3. Using the point-slope form to determine the equation,

       y - y₁ = m(x - x₁)

Substituting the known values,

       y - -2 = (-4/3)(x - 4)

Simplifying,
    y + 2 = (-4/3)(x - 4)
         3y + 6 = -4x + 16
     
 Answer: 4x + 3y = 10