Question

What are the coordinates of the point 3 units from the y-axis and at a distance sqrt5 from (5, 3)?

Answer 1

Simply use the fact -
distance between (3,y) and (5,3) = sqrt(5)

You'll get two such points.

Answer 2

(3,y) are you looking for y ?

Answer 3

let \[a(3,y) ,b(5,3)\]
\[d(a,b)=\sqrt(5-3)^2+(3-y)^2=\sqrt5\]

Answer 4

\[y^2-6y+8=0\]

Answer 5

\[\Delta=36-4(8)=4\]
\[y=2\] or \[y=4\]
\[a(3,4) , a(3,2)\]