please help me solve the question !!

Question

How many lines on the coordinate plane that has distance 1 to the origin O(0,0) and distance 2 to the point A(3,0)  ??

 

(a) 1    (b) 2    (c) 3    (d) 4    (e) infinitely many 

 

 

Answer 1

x=1 is a line that's a distance 1 to the origin and a distance 2 to the point (3,0)

So, there's one line, x=1

to check

use the distance formula, find a point (x,y) that's a distance 1 to (0,0) and 2 to (3,0)

d^2 = x^2 + y^2 = 1

and d^2 = (x-3)^2 + y^2 = 2^2

solve for x and y to get a point on a line

x^2 -6x + 9 + y^2 = 4

x^2 + y^2 = 1 subtract to get

-6x + 9 = 3 or

-6x = -6

x = 1

y^2 = 1-1 = 0

the point (1,0) is the only point on a line that has the specified distances to (0,0) and (3,0)

and there's only one line that will go through that point that's perpendicular to the x axis