Given a circle: C(1,2) & radius #sqrt(5)# a) Find the perpendicular distance from center to #x + 2y -10=0#, show this line is a tangent to the circle. b) Find the perpendicular distance from center to #x+2y -12 =0#, show the line does not meet circle?

1 Answer
Nov 14, 2016

The distance of C to the first line is exactly #sqrt5=radius#, so it is tangent, the distance of C to the second line is #7/5sqrt(5)> sqrt5=radius# so it is external

Explanation:

The general formula for the distance of the generis point #P(x_0;y_0)# to the line #ax+by+c# is

#d=abs(ax_0+by_0+c)/sqrt(a^2+b^2)#

so the distances are

#d_1=abs(1+4-10)/sqrt5=5/sqrt5=sqrt5#

#d_2=abs(1+4-12)/sqrt5=7/sqrt5=7/5sqrt5#