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

We know that , every point on the X-axis in the from (x,0). Let P(x.0) the point on the X-axis have `2sqrt(5)` distance from the point Q(7,-4).
by given condition , PQ`=2sqrt(5)` [`:'` distance formula `=sqrt((x_(2)-x_(1))^(2)+(y_(2)-y_(1))^(2))]`
`rArr(PQ)^(2)=4xx5`
`rArr (x-7)^(2)+(0+4)^(2)=20`
`rArr x^(2)+49-14x+16=20`
`rArr x^(2)-14x-65-20=0`
`rArr x^(2)-14x+45=0`
`rArr x^(2)-9x-5x+45=0`
[by factorisation method]
`rArr x(x-9)-5(x-9)=0`
`rArr (x-9)(x-5)=0`
`:. x=5,9`
Hence , threre are two points lies on the axis , which are (5,0) and (9,0), have `2sqrt(5)` distance from the point (7,-4).