Question

Find the equation for the set of points whose distance from the y-axis equals the distance from the xz-plane.

Answer 1

Answer:

$x_1^2 + z_1^2 = y_1^2$

Step-by-step explanation:

Let   $p(x_1, y_1, z_1)$  be the point.

Any point on y-axis is (0, y, 0)

So, distance is

= $\sqrt{x_1^2+0 + z_1^2}$

= $\sqrt{x_1^2 + z_1^2}$   ......(1)

Now any point on x-z plane is $( x_1, 0, z_1 )$

Distance from p to this point is

= $\sqrt{0+y_1^2 + 0}$

= $\sqrt{y_1^2}$    .........(2)

Equating (1) and (2), we get

$\sqrt{x_1^2 + z_1^2} = \sqrt{y_1^2}$

$x_1^2 + z_1^2 = y_1^2$

This is the required equation.