Question

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

Answer 1

y = (-4/3)(x -4) -2

Explanation:

The slope of the radius to point D is ...

m = (change in y)/(change in x) = (1-(-2))/(8-4) = 3/4

The slope of the perpendicular line will be the negative reciprocal of this:

m' = -1/m = -1/(3/4) = -4/3

The point-slope form of the equation for a line with slope m through point (h, k) can be written as ...

y = m(x -h) +k

We want a line with slope m' through point C:

y = (-4/3)(x -4) -2