Given a circle: C(1,2) & radius sqrt(5)5 a) Find the perpendicular distance from center to x + 2y -10=0x+2y10=0, show this line is a tangent to the circle. b) Find the perpendicular distance from center to x+2y -12 =0x+2y12=0, show the line does not meet circle?

1 Answer
Nov 14, 2016

The distance of C to the first line is exactly sqrt5=radius5=radius, so it is tangent, the distance of C to the second line is 7/5sqrt(5)> sqrt5=radius755>5=radius so it is external

Explanation:

The general formula for the distance of the generis point P(x_0;y_0)P(x0;y0) to the line ax+by+cax+by+c is

d=abs(ax_0+by_0+c)/sqrt(a^2+b^2)d=|ax0+by0+c|a2+b2

so the distances are

d_1=abs(1+4-10)/sqrt5=5/sqrt5=sqrt5d1=|1+410|5=55=5

d_2=abs(1+4-12)/sqrt5=7/sqrt5=7/5sqrt5d2=|1+412|5=75=755