Chapter 10: Tangents and Normals

                                    to the Conic Sections

Beverly B
5th period ICM honors
Ms. Blackwell

  If the Angel is standing at the center of the world (0,0) and needs to find the "highway to heaven", which is eight miles east and five miles north, tangent to the edge of the Earth and runs straight through Rent-a-Car-heaven. Determine the equation to this highway.

-First determine what equation to use:  Equation of the Tangent to a circle: x^2+y^2=r^2 is xx1+yy1-r^2=0. 

-since you the x and y, plug them into the equations:

Eight miles east and five miles north is represented (8,5), which are you x and y :

radius=(8)^2+(5)^2
            64+25
  =sq.root(89) ----> since you found the radius, now plug it into the second formula:
   x(8)+y(5)-(sq.root 89)^2=0
    8x+5y-89=0 <----this is your equation representing the highway.  
                                                                                           

 

Since you figured out how to find the equation of a line, you can find the length of the tangent line from (8,5), to the circle with the following equation : 8x+5y=89.

 

-Figure out the equation needed: length of a segment tangent to a circle:
       t = sq. root((x1-h)^2+ (y1-k)^2-r^2)
-Plug in the information given into the equations: t = sq. root((x1-h)^2+ (y1-k)^2-r^2)
                 ((8-0)^2+ (5-0)^2-(89)^2)
                   (64)+ (25)-(7921)
     = sq. root(7832) or about 88.49 units

 

"Real knowledge is to know the extent of one's ignorance."                  
-Confucius 

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