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

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

1 Answer
Mar 12, 2018

Please see below.

Explanation:

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.