Please Help with the following question.... It is a practice problem that I would like to solve:

Find the equation of a line tangent to the circle (x+1)^2+(y-4)^2=25 at the point (3, 1)

Appreciate you guys

Guest Sep 30, 2017

#1**+2 **

The center of the circle is ( -1, 4 )

And the given point is ( 3, 1 )

Finding the slope between these two points, we have

[ 4 - 1 ] / [ -1 - 3] = [ 3] / [-4] = -3/4

And the slope of the tangent ine will be the negative reciprocal of this = 4/3

So.....the equation of the tangent line is :

y = (4/3) (x - 3) + 1 simplify

y = (4/3)x - 4 + 1

y = (4/3)x - 3

Here's the graph : https://www.desmos.com/calculator/5u5jc97jd5

CPhill Sep 30, 2017