Question 983085: Find the equations of the circles passing through the points(2,3)and the lines
3x-4y+1=0,4x+3y-7=0 touching
Answer by Edwin McCravy(20059)   (Show Source):
You can put this solution on YOUR website! Find the equations of the circles passing through the points(2,3) tangent
to the lines:
3x-4y+1=0, 4x+3y-7=0
Let the center be (h,k) the the radius is the perpendicular distance from
(h,k) to each line. So using the formula:
d = 
r =   
r =  
And since (2,3) is on the circle, the distance from (h,k) to (2,3) also
equals r. use
Square all three sides of
 
So we have the two equations:
Its a lot of work but when you solve those for h and k, you get
h=2, k=8, r=5 and  ,  , r=1
So the circles's equations are
 and 
Edwin
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