Question

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

Answer 1

Let the pt. be (x, 0) then

$\sqrt{(7-x^2)+(-4-0{)}^2}=2\sqrt{5}$

$49+x^2-14x+16=(2\sqrt{5}{)}^2=20$

$x^2=14x+45=0$

$x^2-9x-5x+45=0$

$x(x-9)-5(x-9)=0$

$(x-5)(x-9)=0$

$x=5$ or $x=9$

$\therefore$ pt. is $(5,0)$ or $(9,0)$

$\therefore 2$ pts. are there