find the number of points on x-axis which are at a distance of 2 units from (2,4)

Question

 find the number of points on x-axis which are at a distance of 2 units from (2,4). i want the step by step process

Answer 1

There are no such points.  The x-axis is 4 units from (2,4), so there are no points on the x-axis that are 2 units from (2,4).  You can plot this and see that is the case.

Answer 2

0.

There are no such points. A distance between point (2,  4) and any point on x-axis is at least 4 units. (2, 4) is 4 unit far from the closest point on x-axis, (2,0).

Answer 3

(2,4) is 4 units away from the x-axis. There are no points on the x-axis that are 2 units away from (2,4).

The closest is (2,0)

 

 

You can have a circle with radius 2 and centered at (2,4).

That will give you ALL of the points that are exactly 2 units away from (2,4)

 

 

  The equation of this circle is (x-2)^2 + (y-4)^2 = 4

 

 Now you can generate an unlimited number of points that are

exactly 2 units away from (2,4) by selecting a value for x or y

and then solving.

 

For example, if x=0 then y=4, so (0,4) is exactly 2 units away from (2,4)

if y=0, then   (x-2)^2 + 16 = 4

                    (x-2)^2 = -12

     So the circle does not intersect the x axis, as described in the opening statement

    in bold above