Verified answer

The key point here is that the tangent to a circle is perpendicular to the radius at the contact point.

The circle has center (1,4); the slope from the center to the contact point of (4,8) is....

m = (8 - 4) / (4 - 1) = 4/3

Therefore the tangent line will have a slope of -3/4 and will have the form y = -(3/4)x + b

Substituting the values from the point (4,8) we have

8 = -(3./4)(4) + b

8 = -3 + b

b = 11

So the equation of the tangent line to the given circle is

y = -(3/4)x + 11

ANSWER

y = -(3/4)x + 11

Hope that helps!

Ditto on that one

That looks right.

y=-0.75x+11