How to show that the line 3x+4y=20 is a tangent to the circle x^2+y^2=16?

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Show that the line 3x+4y=20 is a tangent to the circle #x^2+y^2=16#

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Answer 1 · 2018-03-12T14:49:55

Please see below.

The center of the circle #x^2+y^2=16# is #(0,0)# and radius is #4#.

Now let us find the distance of line #3x+4y=20# i.e. #3x+4y-20=0# from #(0,0)#, which is

#|(3*0+4*0-20)/sqrt(3^2+4^2)|#

= #|(-20)/5|=4#

As the distance of center #(0,0)# from #3x+4y=20# is equal to radius #4#,

the line #3x+4y=20# is a tangent to circle #x^2+y^2=16#.