+0  
 
0
36
3
avatar+47 

A circle’s equation is represented by (x - 4)2 + (y + 1)2 = 25. Find the equation of the two tangent lines that have slopes of -¾.

 May 5, 2020
 #1
avatar+111326 
+2

(x - 4)^2  + (y + 1)^2  = 25

 

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

 

We  can use the negative  reciprocal slope to  -3/4 =4/3  to  find the  points  where the tangent lines touch the  circle 

 

If we move 3 units to the right on x  and 4  units up on y from the center we will have the first point where a tangent line touches  this  circle    = ( 7, 3)

 

Likewise....if  we  move  3 units to the left and 4 units down from the center we will have the second point where a tangent line touches the circle  = ( 1, -5)

 

The equation of the  first line is

 

y = (-3/4)(x - 7) + 3

 

The equation of the second line is   

 

y =(-3/4)(x - 1)  -5

 

See the graph here  :  https://www.desmos.com/calculator/mztyclw9nw

 

cool cool cool

 May 5, 2020
 #2
avatar+47 
0

Thank you!

ava27  May 5, 2020
 #3
avatar+111326 
0

No prob, ava    !!!!

 

 

cool cool cool

CPhill  May 5, 2020

22 Online Users

avatar