Question

Find the points on $x$ axis which are at distance of $2\sqrt{5}$ units from the points $(7,-4)$. How many such points are there.

Answer 1

Let Point $P=(x,0)$

$A=(7,-4)$

Given $A=(7,-4)$

$AP=2\sqrt{5}$

${(x-7)}^2+4^2=20$

${(x-7)}^2=20-16=4$

$x-7-2x-7=-2$

$x=9x=5$

$(9,0)(5,0)$

$\therefore$Two such points are there $(9,0)$ & $(5,0)$