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=16x2+y2=16

1 Answer
Mar 12, 2018

Please see below.

Explanation:

The center of the circle x^2+y^2=16x2+y2=16 is (0,0)(0,0) and radius is 44.

Now let us find the distance of line 3x+4y=203x+4y=20 i.e. 3x+4y-20=03x+4y20=0 from (0,0)(0,0), which is

|(3*0+4*0-20)/sqrt(3^2+4^2)|∣ ∣30+402032+42∣ ∣

= |(-20)/5|=4205=4

As the distance of center (0,0)(0,0) from 3x+4y=203x+4y=20 is equal to radius 44,

the line 3x+4y=203x+4y=20 is a tangent to circle x^2+y^2=16x2+y2=16.