Question

I need help with #12 b

Answer 1

Answer:

y = 2x -33

Step-by-step explanation:

The line segment from the center (6, 4) to the given point (16, -1) is a radius of the circle. It is perpendicular to the tangent. Hence you need to write the equation of a line through point (16, -1) that is perpendicular to the line through that point and (6, 4).

The slope of the radius is ...

... ∆y/∆x = (-1-4)/(16-6) = -5/10 = -1/2

The slope of the tangent is the negative reciprocal of that, so is ...

... m = -1/(-1/2) = 2

In point-slope form, the tangent line through (16, -1) is

... y = m(x -h) +k

... y = 2(x -16) +(-1)

Simplifying, this is ...

... y = 2x -33