Find the points on the X-axis which are at distance of `2sqrt(5)` from the point (7,-4) . How many such points are there ?

Explanation

Let P (x,0) be the required point on X-axis.
Let A be the point (7,-4)
Given that, `" "PA=2sqrt5`
`implies" "PA^(2)=20`
`implies" "(x-7)^(2)+(0+4)=20`
`implies" "(x-7)^(2)=20-16=4`
`implies" "x-7=+-2`
`implies" "x=9or x=5`
`therefore` There are two such points.
and points are `(9,0) and(5,0).`