+0  
 
0
56
1
avatar

Calculate the length of a tangent to the circle: x^2+y^2+8x−2y−8=0 at its point of tangency from the point P(2,4)

 Jan 29, 2021
 #1
avatar+116126 
+1

See the graph here  :

 

This is a circle  with a radius of   5   centered  at  (-4,1)

 

The  distance  from  this center to  (2.4)   is a hypotenuse  of a right triangle.......the  radius of the  circle   forms one leg and  the distance from  (2,4)  to the point of tangency  is the other  leg

 

Distance^2  from   (-4,1)  to  (2,4) =     (2 + 4)^2  +  ( 4 - 1)^2 =   36 + 9   = 45

 

So...using the  Pythagorean Theorem,  the  length^2 of the other  leg is

 

45   -  5^2  =     45 -  25  =   20

 

And the sqrt  of this is the distance from   (2,4)  to  the point of tangency =  sqrt (20)  = 2sqrt (5)

 

Here's a graph  :  

 

 

cool cool cool

 Jan 29, 2021

51 Online Users

avatar
avatar