SOLUTION: What is the equation of a line that is tangent to the circle (x-2)2 + y2= 25 at the point (6,3)?

Question 310821: What is the equation of a line that is tangent to the circle (x-2)2 + y2= 25 at the point (6,3)?
Answer by Earlsdon(6294) (Show Source): You can put this solution on YOUR website!
Find the equation of the tangent to the circle at the point (6,3)
Using implicit differentiation, we get:
Solve for the tangent (slope),
and, at the point (6,3) the slope is:
or Now find the equation of the line with slope and containing the point (6,3).
Substitute , and
Simplify and solve for b.

The final equation, in slope-intercept form is:

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But there is a simpler way to do this!
Find the equation of the line that is perpendicular to the radius of the circle and which contains the point (6,3).
Recall that the tangent to a circle is perpendicular to the radius at the point of tangency.
Find the slope of the radius whose end points are the circle center at (2,0) and the point of tangency at (6,3).

The line that's perpendicular to this has a slope that's the negative reciprocal of and this is, so you can start with...
Now substitute the x- and y-coordinates of the point of tangency (6,3).
Simplify and solve for b.
so...

The equation is then...

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