Answer:
[tex]$ x_1^2 + z_1^2 = y_1^2$[/tex]
Step-by-step explanation:
Let [tex]$ p(x_1, y_1, z_1)$[/tex] be the point.
Any point on y-axis is (0, y, 0)
So, distance is
= [tex]$ \sqrt{x_1^2+0 + z_1^2} $[/tex]
= [tex]$ \sqrt{x_1^2 + z_1^2} $[/tex] ......(1)
Now any point on x-z plane is [tex]$ ( x_1, 0, z_1 ) $[/tex]
Distance from p to this point is
= [tex]$ \sqrt{0+y_1^2 + 0} $[/tex]
= [tex]$\sqrt{y_1^2}$[/tex] .........(2)
Equating (1) and (2), we get
[tex]$ \sqrt{x_1^2 + z_1^2} = \sqrt{y_1^2}$[/tex]
[tex]$ x_1^2 + z_1^2 = y_1^2$[/tex]
This is the required equation.
