SOLUTION: find equation of the circle that satisfies the given condition A. tangent 3x-4y=10 and center at c(0,5)

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Question 1085055: find equation of the circle that satisfies the given condition
A. tangent 3x-4y=10 and center at c(0,5)
Found 2 solutions by Fombitz, ikleyn:
Answer by Fombitz(32388)   (Show Source): You can put this solution on YOUR website!
Find the perpendicular line that contains the center.


Perpendicular lines have slopes that are negative reciprocals,


Use the point slope form of a line,


Find the intersection point of the two lines,




So then,




Use the distance formula to find the distance between the two points (the radius of the circle),





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Answer by ikleyn(52915)   (Show Source): You can put this solution on YOUR website!
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find equation of the circle that satisfies the given condition
A. tangent 3x-4y=10 and center at c(0,5)
~~~~~~~~~~~~~~~~~~ 

1.  Find the distance from the point (0,5) to the given line 3x - 4y = 10.


    For it, use the formula on the distance from the given point to the given line of the lesson
        The distance from a point to a straight line in a coordinate plane 
    in this site.


    You will get

    distance =  =  = 4.


    Thus you found the radius of the circle. It is 4 units.


2.  Then the equation of the circle is 

     = ,     or


     = 16.


The solution by the other tutor is not correct, unfortunately.


To see more solved problem of this type, look into the lesson
    - Find the standard equation of a circle
in this site.


Also,  you have this free of charge online textbook in ALGEBRA-II in this site
    ALGEBRA-II - YOUR ONLINE TEXTBOOK.

The referred lesson is the part of this online textbook under the topic
"Conic sections: Ellipses. Definition, major elements and properties. Solved problems".



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