The center of a circle is the point A(-2,1) and point B(-5,-4) is a point on the circle. Find the equation of the line tangent to the circle at the point B.

Question

Point B is on a 90 degree angel.

Answer 1

Hi Joel,

 

   The center of a circle is the point A(-2,1) and point B(-5,-4) is a point on the circle. Find the equation of the line tangent to the circle at the point B. 

 

 

A line that is perpendicular (at a 90 degree angle) has a slope that is the negative reciprocal.

 

So first find the slope of the two points:

 

m=  y₂ - y₁ =  -4 - 1 =  -5  = 5

      -------      ------     ---    --

       x₂- x₁     -5 -(-2)   -3     3 

   

The negative reciprocal is -3/5

                                    

                                    

 

Now find the equation of the line that goes through point B (-5,-4) using slope-intercept form.

 

                     y=mx+b

 

                    y = -3/5 x  + b

                         

 

                    -4= -3/5 (-5) + b

                          

                    -4=3 + b

                     -7=b

 

So the equation is  y = (-3/5) x -7

                                  

 

Hopes the process helps.

THINK MATH!